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Amusements in Mathematics
Amusements in Mathematics

Chapter XIX

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Context Illustration Reading 1/84 · 5 lines
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290.--BOARDS WITH AN ODD NUMBER OF SQUARES.
There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.
Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.
At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.
Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.
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LEARNER DICTIONARY
Archivist
/ˈɑːrkɪvɪst/
Editorial verification pending

A keeper or guardian of historical records and memories.

Amusements in Mathematics

Chapter XIX

Reading 1/84 · 5 reading units · Lines 1–5

Line 1
290.--BOARDS WITH AN ODD NUMBER OF SQUARES.
Line 2
There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.
Line 3
Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.
Line 4
At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.
Line 5
Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

Learner Dictionary

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

Different noun US /ˈdifferent/

a story-specific word describing an important person, object, action, or idea in this passage

From this reading “There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.”

Himself pronoun US /hɪmˈself/

used when the man or boy doing the action is also its object

From this reading “Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.”

Must modal verb US /mʌst/

used to say something is necessary, or almost certainly true

From this reading “At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.”

Pieces noun US /pieces/

an important story-specific word used in this passage

From this reading “There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.”

Point noun US /pɔɪnt/

the main matter or purpose being discussed

From this reading “At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.”

Same noun US /same/

an important story-specific word used in this passage

From this reading “There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.”

These determiner US /ðiːz/

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

From this reading “Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.”

Through noun US /ˈthrough/

a story-specific word describing an important person, object, action, or idea in this passage

From this reading “At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.”

Whatever determiner US /ˌwʌˈtevər/

any or all of a kind, it does not matter which

From this reading “At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.”

Without preposition US /wɪˈθaʊt/

not having, not using, or not accompanied by

From this reading “Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.”

All words in this reading · 80

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 Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

290

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

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

5

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

adeterminerUS /ə/

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

all

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

allow

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

always

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

ANdeterminerUS /æn/

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

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

andconjunctionUS /ənd/

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

areauxiliary verbUS /ɑːr/

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

AtprepositionUS /æt/

in or near a particular place or position

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

board

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

BOARDS

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

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

bottom

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

butconjunctionUS /bʌt/

used to introduce something that contrasts with what came before

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

central

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

centre

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

cut

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

cutting

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

diagrams

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

differentnounUS /ˈdifferent/

a story-specific word describing an important person, object, action, or idea in this passage

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

difficulty

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

draw

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

edge

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

enable

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

end

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

enter

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

enters

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

exactly

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

fifteen

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

Fig

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

forprepositionUS /fɔːr/

intended to be given to, or used by, somebody

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

give

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

himselfpronounUS /hɪmˈself/

used when the man or boy doing the action is also its object

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

IpronounUS /aɪ/

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

ifconjunctionUS /ɪf/

on condition that; in the event that

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

inprepositionUS /ɪn/

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

intoprepositionUS /ˈɪntuː/

moving to the inside of something

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

itpronounUS /ɪt/

a thing, animal, or idea already mentioned

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

leave

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

Limitations

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

line

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

mepronounUS /miː/

the person speaking, as the object of a verb or preposition

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

mustmodal verbUS /mʌst/

used to say something is necessary, or almost certainly true

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

notadverbUS /nɑːt/

used to make a word, phrase, or sentence negative

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

NUMBER

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

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

ODD

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

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

OFprepositionUS /ʌv/

belonging to, or connected with, somebody or something

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

onprepositionUS /ɑːn/

touching and supported by a surface

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

opposite

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

out

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

pieces

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

pointnounUS /pɔɪnt/

the main matter or purpose being discussed

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

reader

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

removed

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

samenounUS /same/

an important story-specific word used in this passage

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

see

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

shape

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

size

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

slightest

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

space

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

square

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

SQUARES

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

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

thedeterminerUS /ðə/

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

thempronounUS /ðem/

the people or things already mentioned, as the object

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

There

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

thesedeterminerUS /ðiːz/

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

throughnounUS /ˈthrough/

a story-specific word describing an important person, object, action, or idea in this passage

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

Thus

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

toparticleUS /tuː/

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

top

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

two

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

ways

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

whateverdeterminerUS /ˌwʌˈtevər/

any or all of a kind, it does not matter which

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

willmodal verbUS /wɪl/

used to talk about the future, or about willingness

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

WITHprepositionUS /wɪð/

in the company of; together with

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

withoutprepositionUS /wɪˈθaʊt/

not having, not using, or not accompanied by

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

x

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

youpronounUS /juː/

the person or people being spoken to

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

yourdeterminerUS /jɔːr/

belonging to the person or people being spoken to

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.