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Amusements in Mathematics
Amusements in Mathematics

Chapter XXII

Cover illustration for Amusements in Mathematics
Context Illustration Reading 1/82 · 5 lines
English subtitles · tap any word to listen 1 / 5
But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.
Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.
Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.
412.--THE MAGIC KNIGHT'S TOUR.
+----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |
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AI-generated narration by OpenAI · Slow US English
LEARNER DICTIONARY
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/ˈɑːrkɪvɪst/
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A keeper or guardian of historical records and memories.

Amusements in Mathematics

Chapter XXII

Reading 1/82 · 5 reading units · Lines 1–5

Line 1
But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.
Line 2
Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.
Line 3
Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.
Line 4
412.--THE MAGIC KNIGHT'S TOUR.
Line 5
+----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

Learner Dictionary

Oxford-style entry order: headword, part of speech, US IPA, concise definition, contextual example, audio, and collocations from this reading.

Consecutive adjective US /kənˈsɛk.jə.tɪv/

Following continuously in unbroken sequence.

From this reading “But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.”

Even noun US /even/

an important story-specific word used in this passage

From this reading “Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.”

Have auxiliary verb US /hæv/

used with a past participle to form the perfect tenses

From this reading “But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.”

Order noun US /order/

an important story-specific word used in this passage

From this reading “Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.”

Quite noun US /quite/

an important story-specific word used in this passage

From this reading “Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.”

Required noun US /required/

an important story-specific word used in this passage

From this reading “Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.”

These determiner US /ðiːz/

the plural of “this”: the people or things near, or just mentioned

From this reading “But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.”

Though conjunction US /ðoʊ/

in spite of the fact that

From this reading “Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.”

Without preposition US /wɪˈθaʊt/

not having, not using, or not accompanied by

From this reading “Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.”

Yet conjunction US /jet/

but in spite of that

From this reading “Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.”

All words in this reading · 109

Every word is available to listen to. Dictionary details are shown only when verified; these are not licensed Oxford entries.

1

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

1,327

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

10

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

10,000

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

11

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

12

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

16

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

17

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

18

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

19

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

20

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

21

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

22

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

23

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

24

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

25

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

41

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

412

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading 412.--THE MAGIC KNIGHT'S TOUR.

42

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

43

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

44

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

45

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

46

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

47

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

48

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

5

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

52

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

523

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

53

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

54

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

55

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

56

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

57

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

58

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

59

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

6

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

60

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

7

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

8

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

9

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading +----+----+----+----+----+----+----+----+ | 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 | +----+----+----+----+----+----+----+----+ | 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 | +----+----+----+----+----+----+----+----+ | 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 | +----+----+----+----+----+----+----+----+ | 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 | +----+----+----+----+----+----+----+----+ | 52 |

adeterminerUS /ə/

used before a singular noun to mean one of a group, when it is not a particular one

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

accelerating

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From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

add

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From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

andeterminerUS /æn/

the form of “a” used before a word that begins with a vowel sound

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

andconjunctionUS /ənd/

used to join words or parts of a sentence that go together

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

answers

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

areauxiliary verbUS /ɑːr/

the form of “be” used with you, we, they, or a plural noun

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

asconjunctionUS /æz/

at the same time that; because; in the way that

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

big

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From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

ButconjunctionUS /bʌt/

used to introduce something that contrasts with what came before

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

byprepositionUS /baɪ/

showing who or what does the action

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

case

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

composites

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

consecutiveadjectiveUS /kənˈsɛk.jə.tɪv/

Following continuously in unbroken sequence.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

difficulty

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From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

eachdeterminerUS /iːtʃ/

every one of two or more people or things, taken separately

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

EvennounUS /even/

an important story-specific word used in this passage

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

find

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

forprepositionUS /fɔːr/

intended to be given to, or used by, somebody

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

form

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From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

get

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

haveauxiliary verbUS /hæv/

used with a past participle to form the perfect tenses

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

hundred

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

IpronounUS /aɪ/

the person speaking or writing, as the subject of the verb

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

ifconjunctionUS /ɪf/

on condition that; in the event that

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

inprepositionUS /ɪn/

inside something, or within a place, period, or state

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

increases

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

isauxiliary verbUS /ɪz/

the form of “be” used with he, she, it, or a singular noun

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

itpronounUS /ɪt/

a thing, animal, or idea already mentioned

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

KNIGHT'S

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From this reading 412.--THE MAGIC KNIGHT'S TOUR.

larger

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

magic

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

matter

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

means

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

notadverbUS /nɑːt/

used to make a word, phrase, or sentence negative

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

numbers

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

ofprepositionUS /ʌv/

belonging to, or connected with, somebody or something

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

ordernounUS /order/

an important story-specific word used in this passage

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

possible

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

process

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

quitenounUS /quite/

an important story-specific word used in this passage

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

ratio

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

requirednounUS /required/

an important story-specific word used in this passage

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

said

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

search

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

shouldmodal verbUS /ʃʊd/

used to say what is right, expected, or advisable

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

shown

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

simple

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

sixteen

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

smallest

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

square

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

success

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

suchdeterminerUS /sʌtʃ/

of the kind already mentioned

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

tables

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

task

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

thedeterminerUS /ðə/

used before a noun that is already known, already mentioned, or the only one of its kind

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

thesedeterminerUS /ðiːz/

the plural of “this”: the people or things near, or just mentioned

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

thirty-six

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

thoughconjunctionUS /ðoʊ/

in spite of the fact that

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

toparticleUS /tuː/

used before the base form of a verb to make the infinitive

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

TOUR

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading 412.--THE MAGIC KNIGHT'S TOUR.

twenty-five

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

up

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

wepronounUS /wiː/

the speaker together with one or more other people

From this reading But, as I have said, these are not the answers in the smallest numbers: for if we add 523 to the numbers 1 to 16, we get sixteen consecutive composites; and if we add 1,327 to the numbers 1 to 25, we get twenty-five consecutive composites, in each case the smallest numbers possible.

willmodal verbUS /wɪl/

used to talk about the future, or about willingness

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

withprepositionUS /wɪð/

in the company of; together with

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

withoutprepositionUS /wɪˈθaʊt/

not having, not using, or not accompanied by

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.

YetconjunctionUS /jet/

but in spite of that

From this reading Yet if we required to form a magic square of a hundred such numbers, we should find it a big task by means of tables, though by the process I have shown it is quite a simple matter.

youpronounUS /juː/

the person or people being spoken to

From this reading Even to find thirty-six such numbers you will search the tables up to 10,000 without success, and the difficulty increases in an accelerating ratio with each square of a larger order.