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Amusements in Mathematics
Amusements in Mathematics

Chapter III · Chapter 3

Chapter 3 of Amusements in Mathematics is here in full — 417 sentences across 84 reading sections, with audio for every sentence and word.

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Context Illustration Reading 1/83 · 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 · Chapter 3

Chapter 3 of Amusements in Mathematics is here in full — 417 sentences across 84 reading sections, with audio for every sentence and word.

Reading 1/83 · 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.
/juːs ˈevəri wʌn ʌv ðə naɪn ˈdɪdʒəts wʌns ənd ˈoʊnli wʌns ɪn ˈevəri keɪs/
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

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.

containing verb US /kənˈteɪnɪŋ/

-ing form of “contain” — include or contain; have as a component

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 adjective US /ˈdɪdʒətəl/

displaying numbers rather than scale positions

From this reading “92.--DIGITAL SQUARE NUMBERS.”

digits noun US /ˈdɪdʒəts/

plural of “digit” — one of the elements that collectively form a system of numeration

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.”

fraction noun US /ˈfrækʃən/

a component of a mixture that has been separated by a fractional process

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 adjective US /mɪkst/

consisting of a haphazard assortment of different kinds

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.”

published adjective US /ˈpʌblɪʃt/

prepared and printed for distribution and sale

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 verb US /ˈpʌzəl/

be a mystery or bewildering 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.”

solution noun US /səˈluːʃən/

a homogeneous mixture of two or more substances; frequently (but not necessarily) a liquid solution

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 words in this reading · 69

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.

100

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.

13

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.

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.

alladjectiveUS /ɔːl/

(quantifier) used with either mass or count nouns to indicate the whole number or amount of or every one of a class

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.

arrangedadjectiveUS /ərˈeɪndʒd/

disposed or placed in a particular kind of order

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.

attemptnounUS /əˈtempt/

earnest and conscientious activity intended to do or accomplish 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.

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.

casenounUS /keɪs/

an occurrence of something

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

containingverbUS /kənˈteɪnɪŋ/

-ing form of “contain” — include or contain; have as a component

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.

DIGITALadjectiveUS /ˈdɪdʒətəl/

displaying numbers rather than scale positions

From this reading 92.--DIGITAL SQUARE NUMBERS.

digitsnounUS /ˈdɪdʒəts/

plural of “digit” — one of the elements that collectively form a system of numeration

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.

expressionnounUS /ɪkˈspreʃən/

the feelings expressed on a person's face

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.

firstadjectiveUS /fɜːrst/

preceding all others in time or space or degree

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.

formnounUS /fɔːrm/

the phonological or orthographic sound or appearance of a word that can be used to describe or identify something

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

fournounUS /fɔːr/

the cardinal number that is the sum of three and one

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

fractionnounUS /ˈfrækʃən/

a component of a mixture that has been separated by a fractional process

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.

handnounUS /hænd/

the (prehensile) extremity of the superior limb

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.

HereadverbUS /hiːr/

in or at this place; where the speaker or writer is

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.

lastadjectiveUS /læst/

immediately past

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.

lednounUS /led/

diode such that light emitted at a p-n junction is proportional to the bias current; color depends on the material used

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.

mixedadjectiveUS /mɪkst/

consisting of a haphazard assortment of different kinds

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.

ninenounUS /naɪn/

the cardinal number that is the sum of eight and 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.

numbersnounUS /ˈnʌmbərz/

the fourth book of the Old Testament; contains a record of the number of Israelites who followed Moses out of Egypt

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.

onceadverbUS /wʌns/

on one occasion

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.

onlyadverbUS /ˈoʊnli/

and nothing more

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

publishedadjectiveUS /ˈpʌblɪʃt/

prepared and printed for distribution and sale

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.

puzzleverbUS /ˈpʌzəl/

be a mystery or bewildering 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.

readernounUS /ˈriːdər/

a person who enjoys reading

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.

solutionnounUS /səˈluːʃən/

a homogeneous mixture of two or more substances; frequently (but not necessarily) a liquid solution

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.

SQUAREverbUS /skwer/

make square

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.

tryverbUS /traɪ/

make an effort or attempt

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.

turnverbUS /tɜːrn/

change orientation or direction, also in the abstract sense

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.

twelvenounUS /twelv/

the cardinal number that is the sum of eleven and one

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.

upadjectiveUS /ʌp/

being or moving higher in position or greater in some value; being above a former position or level

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.

UsenounUS /juːs/

the act of using

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.

Chapter 3 of Amusements in Mathematics by Henry Ernest Dudeney holds 417 sentences, grouped into 84 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 3 of Amusements in Mathematics contain?

Chapter 3 holds 417 sentences of Amusements in Mathematics, unabridged, divided into 84 reading sections.

This page carries chapter 3 of Amusements in Mathematics by Henry Ernest Dudeney exactly as it stands in the source edition, without abridgement. It runs to 417 sentences, grouped into 84 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 3 of Amusements in Mathematics?

Work through the 84 sections in order, replaying any sentence and tapping unfamiliar words for their entries.

Each of the 84 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 3 be read aloud to me?

Yes — every sentence and every individual word in chapter 3 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.

How to read Amusements in Mathematics section by section

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  1. Open a chapter

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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.