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Amusements in Mathematics
Amusements in Mathematics

Chapter XII · Chapter 12

Chapter 12 of Amusements in Mathematics is here in full — 388 sentences across 78 reading sections, with audio for every sentence and word.

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Context Illustration Reading 1/77 · 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).
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LEARNER DICTIONARY
Archivist
/ˈɑːrkɪvɪst/
Editorial verification pending

A keeper or guardian of historical records and memories.

Amusements in Mathematics

Chapter XII · Chapter 12

Chapter 12 of Amusements in Mathematics is here in full — 388 sentences across 78 reading sections, with audio for every sentence and word.

Reading 1/77 · 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."
/ðə fɔːr ˈoʊ.pən ˈspeɪsəz wer fɔːr ˈpæsədʒəz end ɑːr nɑːt ˈrekənd æz ˈpæsədʒəz/
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

These definitions explain words found in the current reading and keep every example grounded in its original sentence.

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

alleys noun US /ˈæliz/

plural of “alley” — a narrow street with walls on both sides

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

annexed verb US /ˈænekst/

past form of “annex” — take (territory) as if by conquest

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

diagram noun US /ˈdaɪəɡræm/

a drawing intended to explain how something works; a drawing showing the relation between the parts

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

dotted adjective US /ˈdɑːtəd/

having a pattern of dots

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 noun US /fɪɡ/

a diagram or picture illustrating textual material

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

maze noun US /meɪz/

complex system of paths or tunnels in which it is easy to get lost

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 noun US /ruːts/

plural of “route” — an established line of travel or access

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?”

Similarly adverb US /ˈsɪmələrli/

in like or similar manner

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.”

All words in this reading · 87

Every word in these five lines is listed here, and every one of them can be played on its own.

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?

affairsnounUS /əˈferz/

matters of personal concern

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

againadverbUS /əˈɡen/

anew

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

alleysnounUS /ˈæliz/

plural of “alley” — a narrow street with walls on both sides

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?

alsoadverbUS /ˈɔːlsoʊ/

in addition

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.

annexedverbUS /ˈænekst/

past form of “annex” — take (territory) as if by conquest

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

anyadjectiveUS /ˈeni/

one or some or every or all without specification

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?

arrivedverbUS /ərˈaɪvd/

past form of “arrive” — reach a destination; arrive by movement or progress

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.

BnounUS /biː/

aerobic rod-shaped spore-producing bacterium; often occurring in chainlike formations; found primarily in soil

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.

blindnounUS /blaɪnd/

people who have severe visual impairments, considered as a group

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.

CnounUS /siː/

a degree on the centigrade scale of temperature

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).

casenounUS /keɪs/

an occurrence of 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.

DnounUS /diː/

a fat-soluble vitamin that prevents rickets

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.

diagramnounUS /ˈdaɪəɡræm/

a drawing intended to explain how something works; a drawing showing the relation between the parts

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

differentadjectiveUS /ˈdɪfərənt/

unlike in nature or quality or form or degree

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?

dottedadjectiveUS /ˈdɑːtəd/

having a pattern of dots

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.

EnounUS /iː/

a fat-soluble vitamin that is essential for normal reproduction; an important antioxidant that neutralizes free radicals in the body

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.

endnounUS /end/

either extremity of something that has length

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

expressverbUS /ɪkˈspres/

give expression to

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

FnounUS /ef/

a degree on the Fahrenheit scale of temperature

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.

FignounUS /fɪɡ/

a diagram or picture illustrating textual material

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

foundverbUS /faʊnd/

set up or found

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.

fournounUS /fɔːr/

the cardinal number that is the sum of three and one

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?

getverbUS /ɡet/

come into the possession of something concrete or abstract

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.

gettingnounUS /ˈɡetɪŋ/

the act of acquiring 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.

goverbUS /ɡoʊ/

change location; move, travel, or proceed, also metaphorically

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?

indicatedverbUS /ˈɪndəkeɪtəd/

past form of “indicate” — be a signal for or a symptom of

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.

littleadjectiveUS /ˈlɪtəl/

limited or below average in number or quantity or magnitude or extent

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

manyadjectiveUS /ˈmeni/

a quantifier that can be used with count nouns and is often preceded by “as” or “too” or “so” or “that”; amounting to a large but indefinite number

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?

markedadjectiveUS /mɑːrkt/

strongly marked; easily noticeable

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.

mazenounUS /meɪz/

complex system of paths or tunnels in which it is easy to get lost

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?

neveradverbUS /ˈnevər/

not ever; at no time in the past or future

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."

NowadverbUS /naʊ/

in the historical present; at this point in the narration of a series of past events

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."

otheradjectiveUS /ˈʌðər/

not the same one or ones already mentioned or implied

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 /ˈpæsədʒ/

the act of passing from one state or place to the next

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?

passagesnounUS /ˈpæsədʒəz/

plural of “passage” — the act of passing from one state or place to the next

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

positionnounUS /pəˈzɪʃən/

the particular portion of space occupied by something

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

reckonedverbUS /ˈrekənd/

past form of “reckon” — expect, believe, or suppose

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

routenounUS /ruːt/

an established line of travel or access

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?

routesnounUS /ruːts/

plural of “route” — an established line of travel or access

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?

sameadjectiveUS /seɪm/

Identical; not different.

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?

seenverbUS /siːn/

inflected form of “see” — perceive by sight or have the power to perceive by sight

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

SimilarlyadverbUS /ˈsɪmələrli/

in like or similar manner

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.

spacesnounUS /ˈspeɪsəz/

plural of “space” — the unlimited expanse in which everything is located

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

starsnounUS /stɑːrz/

plural of “star” — (astronomy) a celestial body of hot gases that radiates energy derived from thermonuclear reactions in the interior

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.

suppressedadjectiveUS /səˈprest/

kept from public knowledge by various means

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?

thereadverbUS /ðer/

in or at that place or location

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?

threenounUS /θriː/

the cardinal number that is the sum of one and one and one

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?

twiceadverbUS /twaɪs/

two times

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?

waysnounUS /weɪz/

structure consisting of a sloping way down to the water from the place where ships are built or repaired

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.

Chapter 12 of Amusements in Mathematics by Henry Ernest Dudeney holds 388 sentences, grouped into 78 reading sections of at most 5 sentences. The text is the source edition, unabridged, and the chapter records which sentences cover which part of the work so that nothing is dropped. Every word can be tapped for its pronunciation and dictionary entry.

What does chapter 12 of Amusements in Mathematics contain?

Chapter 12 holds 388 sentences of Amusements in Mathematics, unabridged, divided into 78 reading sections.

This page carries chapter 12 of Amusements in Mathematics by Henry Ernest Dudeney exactly as it stands in the source edition, without abridgement. It runs to 388 sentences, grouped into 78 sections of at most 5 sentences so that a reader can take the chapter in steady, finishable pieces. The chapter also stores a coverage record mapping every one of its sentences to a part of the work, which is how the edition demonstrates that no line was dropped.

How do I study chapter 12 of Amusements in Mathematics?

Work through the 78 sections in order, replaying any sentence and tapping unfamiliar words for their entries.

Each of the 78 sections in this chapter is short enough to read once, hear once, and then re-read with the vocabulary in view. Tapping a word plays it alone and opens its dictionary entry with IPA, part of speech and meaning, so the reader is never forced to guess a pronunciation from spelling. Working section by section keeps a long chapter from becoming an undifferentiated wall of text, which is the usual reason a reader abandons a work of this period.

Can chapter 12 be read aloud to me?

Yes — every sentence and every individual word in chapter 12 can be played aloud in United States English.

Audio covers the whole chapter: any sentence can be played, and any single word within it can be played on its own. The voice uses United States English. For a work of this period that matters, because spelling is an unreliable guide to pronunciation for vocabulary that has fallen out of daily use, and a learner who guesses wrong tends to keep the error. Hearing the word in its own sentence, and then alone, settles it.

Questions about reading Amusements in Mathematics

Common questions about reading Amusements in Mathematics by Henry Ernest Dudeney on this page, its source edition and its audio.

Is this the complete text of Amusements in Mathematics?

Yes. All 8979 sentences of Project Gutenberg eBook #16713 are kept, with a record of which sentences cover which part.

Which edition of Amusements in Mathematics is used?

Project Gutenberg eBook #16713, unabridged. The Project Gutenberg header, footer and licence are removed.

How long does Amusements in Mathematics take to read?

About 600 minutes of reading across 1796 sections of 5 sentences each, at an unhurried pace.

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Vocabulary met early in Amusements in Mathematics

Words and structures a reader meets early in Amusements in Mathematics, each tappable for pronunciation and meaning.

Common
A word that appears in the opening chapter of Amusements in Mathematics; the reader can tap it to hear it and see its dictionary entry.
Units
A word that appears in the opening chapter of Amusements in Mathematics; the reader can tap it to hear it and see its dictionary entry.
Penny
A word that appears in the opening chapter of Amusements in Mathematics; the reader can tap it to hear it and see its dictionary entry.
Abbreviated
A word that appears in the opening chapter of Amusements in Mathematics; the reader can tap it to hear it and see its dictionary entry.