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Amusements in Mathematics
Amusements in Mathematics

Chapter III

Cover illustration for Amusements in Mathematics
Context Illustration Reading 1/84 · 5 lines
English subtitles · tap any word to listen 1 / 5
When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.
Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.
Use every one of the nine digits once, and only once, in every case.
92.--DIGITAL SQUARE NUMBERS.
Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.
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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 III

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

Line 1
When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.
Line 2
Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.
Line 3
Use every one of the nine digits once, and only once, in every case.
Line 4
92.--DIGITAL SQUARE NUMBERS.
Line 5
Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

Learner Dictionary

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

Every determiner US /ˈevəri/

all the members of a group, with none left out

From this reading “Use every one of the nine digits once, and only once, in every case.”

First noun US /first/

an important story-specific word used in this passage

From this reading “When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.”

Hand noun US /hand/

an important story-specific word used in this passage

From this reading “Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.”

Here noun US /here/

an important story-specific word used in this passage

From this reading “Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.”

Last noun US /last/

an important story-specific word used in this passage

From this reading “When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.”

Mixed verb US /mɪkst/

involved with or connected to

From this reading “When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.”

Once noun US /once/

an important story-specific word used in this passage

From this reading “Use every one of the nine digits once, and only once, in every case.”

One pronoun US /wʌn/

used to mean any person in general, including the speaker

From this reading “Use every one of the nine digits once, and only once, in every case.”

All words in this reading · 69

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

100

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From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

13

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From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

14

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

15

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

16

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

18

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

20

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

27

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

324

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

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

36

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

40

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

576

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

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

69

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

72

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

81

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

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

9

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

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

92

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

From this reading 92.--DIGITAL SQUARE NUMBERS.

94

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

adeterminerUS /ə/

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

all

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

andconjunctionUS /ənd/

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

From this reading Use every one of the nine digits once, and only once, in every case.

areauxiliary verbUS /ɑːr/

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

arranged

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

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

atprepositionUS /æt/

in or near a particular place or position

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

attempt

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

byprepositionUS /baɪ/

showing who or what does the action

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

case

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

From this reading Use every one of the nine digits once, and only once, in every case.

containing

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

DIGITAL

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

From this reading 92.--DIGITAL SQUARE NUMBERS.

digits

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

everydeterminerUS /ˈevəri/

all the members of a group, with none left out

From this reading Use every one of the nine digits once, and only once, in every case.

expression

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

firstnounUS /first/

an important story-specific word used in this passage

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

forprepositionUS /fɔːr/

intended to be given to, or used by, somebody

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

form

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

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

four

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

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

fraction

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

hand

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

HerenounUS /here/

an important story-specific word used in this passage

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

hisdeterminerUS /hɪz/

belonging to a man, boy, or male animal already mentioned

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

IpronounUS /aɪ/

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

inprepositionUS /ɪn/

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

lastnounUS /last/

an important story-specific word used in this passage

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

led

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

mixedverbUS /mɪkst/

involved with or connected to

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

mydeterminerUS /maɪ/

belonging to the person speaking

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

nine

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

numbers

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

ofprepositionUS /ʌv/

belonging to, or connected with, somebody or something

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

once

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

From this reading Use every one of the nine digits once, and only once, in every case.

onepronounUS /wʌn/

used to mean any person in general, including the speaker

From this reading Use every one of the nine digits once, and only once, in every case.

only

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

From this reading Use every one of the nine digits once, and only once, in every case.

published

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

puzzle

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

reader

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

soconjunctionUS /soʊ/

for that reason; with the result that

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

solution

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

SQUARE

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

From this reading 92.--DIGITAL SQUARE NUMBERS.

thatconjunctionUS /ðæt/

used to introduce what somebody said, thought, or felt

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

thedeterminerUS /ðə/

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

theypronounUS /ðeɪ/

the people, animals, or things already mentioned, as the subject

From this reading Here are the nine digits so arranged that they form four square numbers: 9, 81, 324, 576.

toparticleUS /tuː/

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

try

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

turn

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

twelve

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

From this reading Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94.

up

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

Use

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

From this reading Use every one of the nine digits once, and only once, in every case.

wasauxiliary verbUS /wɑːz/

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

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.

WhenconjunctionUS /wen/

at the time that

From this reading When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits.