Complete classic literature • Five-line readings • Clear US narration
VELMORA ACADEMY
Academy of Archival Languages & Memory Studies
Menu Close
Amusements in Mathematics
Amusements in Mathematics

Chapter XII

Cover illustration for Amusements in Mathematics
Context Illustration Reading 1/78 · 5 lines
English subtitles · tap any word to listen 1 / 5
Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?
The four open spaces where four passages end are not reckoned as "passages."
In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.
It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.
We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).
0:00 / 0:00
Speed 0.75x
AI-generated narration by OpenAI · Slow US English
LEARNER DICTIONARY
Archivist
/ˈɑːrkɪvɪst/
Editorial verification pending

A keeper or guardian of historical records and memories.

Amusements in Mathematics

Chapter XII

Reading 1/78 · 5 reading units · Lines 1–5

Line 1
Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?
Line 2
The four open spaces where four passages end are not reckoned as "passages."
Line 3
In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.
Line 4
It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.
Line 5
We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

Learner Dictionary

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

Again noun US /again/

an important story-specific word used in this passage

From this reading “In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.”

Along preposition US /əˈlɔːŋ/

following the length of something from one end toward the other

From this reading “Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?”

Different noun US /ˈdifferent/

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

From this reading “Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?”

Express verb US /ɪkˈspres/

to show or communicate a feeling or idea

From this reading “We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).”

Found noun US /found/

an important story-specific word used in this passage

From this reading “It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.”

Have auxiliary verb US /hæv/

used with a past participle to form the perfect tenses

From this reading “In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.”

Little noun US /little/

an important story-specific word used in this passage

From this reading “We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).”

Must modal verb US /mʌst/

used to say something is necessary, or almost certainly true

From this reading “Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?”

Never noun US /never/

an important story-specific word used in this passage

From this reading “Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?”

Open verb US /ˈoʊ.pən/

To move from a closed position.

From this reading “The four open spaces where four passages end are not reckoned as "passages."”

Passage noun US /ˈpassage/

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

From this reading “Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?”

Same noun US /same/

an important story-specific word used in this passage

From this reading “Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?”

Therefore adverb US /ˈðerfɔːr/

for that reason; as a result

From this reading “We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).”

All words in this reading · 87

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 It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

2

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

22

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

23

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

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

3

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

4

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

5

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

6

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

AdeterminerUS /ə/

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

affairs

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

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

againnounUS /again/

an important story-specific word used in this passage

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

alleys

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

alongprepositionUS /əˈlɔːŋ/

following the length of something from one end toward the other

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

also

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

andconjunctionUS /ənd/

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

annexed

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

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

any

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

areauxiliary verbUS /ɑːr/

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

arrived

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

asconjunctionUS /æz/

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

From this reading The four open spaces where four passages end are not reckoned as "passages."

atprepositionUS /æt/

in or near a particular place or position

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

B

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

beauxiliary verbUS /biː/

used with a past participle to form the passive, or with -ing for continuous tenses

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

blind

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

ButconjunctionUS /bʌt/

used to introduce something that contrasts with what came before

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

byprepositionUS /baɪ/

showing who or what does the action

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

C

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

canmodal verbUS /kæn/

to be able to, or to be allowed to

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

case

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

D

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

diagram

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

differentnounUS /ˈdifferent/

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

dotted

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

E

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

end

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

From this reading The four open spaces where four passages end are not reckoned as "passages."

expressverbUS /ɪkˈspres/

to show or communicate a feeling or idea

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

F

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

Fig

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

foundnounUS /found/

an important story-specific word used in this passage

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

four

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

From this reading The four open spaces where four passages end are not reckoned as "passages."

fromprepositionUS /frʌm/

showing where something starts, or who sent it

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

get

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

getting

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

go

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

haveauxiliary verbUS /hæv/

used with a past participle to form the perfect tenses

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

how

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

IpronounUS /aɪ/

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

ifconjunctionUS /ɪf/

on condition that; in the event that

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

inprepositionUS /ɪn/

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

indicated

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

itpronounUS /ɪt/

a thing, animal, or idea already mentioned

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

littlenounUS /little/

an important story-specific word used in this passage

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

many

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

marked

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

maze

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

mustmodal verbUS /mʌst/

used to say something is necessary, or almost certainly true

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

nevernounUS /never/

an important story-specific word used in this passage

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

notadverbUS /nɑːt/

used to make a word, phrase, or sentence negative

From this reading The four open spaces where four passages end are not reckoned as "passages."

Now

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

ofprepositionUS /ʌv/

belonging to, or connected with, somebody or something

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

openverbUS /ˈoʊ.pən/

To move from a closed position.

From this reading The four open spaces where four passages end are not reckoned as "passages."

other

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

passagenounUS /ˈpassage/

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

passages

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

From this reading The four open spaces where four passages end are not reckoned as "passages."

position

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

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

reckoned

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

From this reading The four open spaces where four passages end are not reckoned as "passages."

route

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

routes

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

samenounUS /same/

an important story-specific word used in this passage

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

seen

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

Similarly

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

spaces

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

From this reading The four open spaces where four passages end are not reckoned as "passages."

stars

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

suppressed

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

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

thatconjunctionUS /ðæt/

used to introduce what somebody said, thought, or felt

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.

thedeterminerUS /ðə/

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

there

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

thereforeadverbUS /ˈðerfɔːr/

for that reason; as a result

From this reading We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).

thisdeterminerUS /ðɪs/

used for a person or thing that is near, or that has just been mentioned

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

three

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

toparticleUS /tuː/

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

twice

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

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

ways

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

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

wepronounUS /wiː/

the speaker together with one or more other people

From this reading Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?

whenconjunctionUS /wen/

at the time that

From this reading It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.

whereconjunctionUS /wer/

in or at the place that

From this reading The four open spaces where four passages end are not reckoned as "passages."

willmodal verbUS /wɪl/

used to talk about the future, or about willingness

From this reading In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.