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Amusements in Mathematics
Amusements in Mathematics

Chapter XXI · Chapter 21

Chapter 21 of Amusements in Mathematics is here in full — 402 sentences across 81 reading sections, with audio for every sentence and word.

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Context Illustration Reading 1/80 · 5 lines
English subtitles · tap any word to listen 1 / 5
On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.
Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.
In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.
Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.
371.--GOLD PACKING IN RUSSIA.
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Amusements in Mathematics

Chapter XXI · Chapter 21

Chapter 21 of Amusements in Mathematics is here in full — 402 sentences across 81 reading sections, with audio for every sentence and word.

Reading 1/80 · 5 reading units · Lines 1–5

Line 1
On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.
Line 2
Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.
Line 3
In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.
Line 4
Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.
Line 5
371.--GOLD PACKING IN RUSSIA.

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.

alternate adjective US /ˈɔːltərnət/

every second one of a series

From this reading “In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.”

alternately adverb US /ˈɔːltərnətli/

in an alternating sequence or position

From this reading “On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.”

balls noun US /bɔːlz/

plural of “ball” — round object that is hit or thrown or kicked in games

From this reading “On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.”

consisting verb US /kənˈsɪstɪŋ/

-ing form of “consist” — originate

From this reading “Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.”

layer noun US /ˈleɪər/

single thickness of usually some homogeneous substance

From this reading “Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.”

layers noun US /ˈleɪərz/

plural of “layer” — single thickness of usually some homogeneous substance

From this reading “In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.”

packing noun US /ˈpækɪŋ/

any material used especially to protect something

From this reading “371.--GOLD PACKING IN RUSSIA.”

russia noun US /ˈrʌʃə/

a former communist country in eastern Europe and northern Asia; established in 1922; included Russia and 14 other soviet socialist republics (Ukraine and Byelorussia and others); officially dissolved 31 December 1991

From this reading “371.--GOLD PACKING IN RUSSIA.”

All words in this reading · 62

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.

1,226

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

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

10

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

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

12

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

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

13

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

14

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

15

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

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

22

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

24

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

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

371

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

From this reading 371.--GOLD PACKING IN RUSSIA.

4

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

5

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

6

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

7

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

78

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

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

8

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

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

85

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

9

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

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

adeterminerUS /ə/

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

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

AboveprepositionUS /əˈbʌv/

higher than, or over, something

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

addedverbUS /ˈædəd/

past form of “add” — make an addition (to); join or combine or unite with others; increase the quality, quantity, size or scope of

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

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 On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

alternateadjectiveUS /ˈɔːltərnət/

every second one of a series

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

alternatelyadverbUS /ˈɔːltərnətli/

in an alternating sequence or position

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

andconjunctionUS /ənd/

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

anotherdeterminerUS /əˈnʌðər/

one more of the same kind, or a different one

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

arrangeverbUS /ərˈeɪndʒ/

put into a proper or systematic order

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

ballsnounUS /bɔːlz/

plural of “ball” — round object that is hit or thrown or kicked in games

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

beauxiliary verbUS /biː/

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

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

boxnounUS /bɑːks/

a (usually rectangular) container; may have a lid

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

byprepositionUS /baɪ/

showing who or what does the action

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

canmodal verbUS /kæn/

to be able to, or to be allowed to

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

consistingverbUS /kənˈsɪstɪŋ/

-ing form of “consist” — originate

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

containingverbUS /kənˈteɪnɪŋ/

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

contentsnounUS /ˈkɑːntents/

(usually plural) everything that is included in a collection and that is held or included in something

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

forprepositionUS /fɔːr/

intended to be given to, or used by, somebody

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

fulladjectiveUS /fʊl/

containing as much or as many as is possible or normal

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

givesnounUS /ɡɪvz/

plural of “give” — the elasticity of something that can be stretched and returns to its original length

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

GOLDnounUS /ɡoʊld/

coins made of gold

From this reading 371.--GOLD PACKING IN RUSSIA.

inprepositionUS /ɪn/

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

inchesnounUS /ˈɪntʃəz/

plural of “inch” — a unit of length equal to one twelfth of a foot

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

layernounUS /ˈleɪər/

single thickness of usually some homogeneous substance

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

layersnounUS /ˈleɪərz/

plural of “layer” — single thickness of usually some homogeneous substance

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

lengthnounUS /leŋkθ/

the linear extent in space from one end to the other; the longest dimension of something that is fixed in place

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

maymodal verbUS /meɪ/

used to say something is possible, or to give permission

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

ofprepositionUS /ʌv/

belonging to, or connected with, somebody or something

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

OnprepositionUS /ɑːn/

touching and supported by a surface

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

orconjunctionUS /ɔːr/

used to join alternatives or possibilities

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

packedadjectiveUS /pækt/

extremely crowed or filled to capacity

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

PACKINGnounUS /ˈpækɪŋ/

any material used especially to protect something

From this reading 371.--GOLD PACKING IN RUSSIA.

placenounUS /pleɪs/

a point located with respect to surface features of some region

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

rowsnounUS /roʊz/

plural of “row” — an arrangement of objects or people side by side in a line

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

RUSSIAnounUS /ˈrʌʃə/

a former communist country in eastern Europe and northern Asia; established in 1922; included Russia and 14 other soviet socialist republics (Ukraine and Byelorussia and others); officially dissolved 31 December 1991

From this reading 371.--GOLD PACKING IN RUSSIA.

sidenounUS /saɪd/

a place within a region identified relative to a center or reference location

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

suchdeterminerUS /sʌtʃ/

of the kind already mentioned

From this reading In the length of 24+9/10 inches 15 such layers may be packed, the alternate layers containing 85 and 78 balls.

thedeterminerUS /ðə/

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

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

thisdeterminerUS /ðɪs/

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

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

ThusadverbUS /ðʌs/

(used to introduce a logical conclusion) from that fact or reason or as a result

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

timesnounUS /taɪmz/

a more or less definite period of time now or previously present

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

toparticleUS /tuː/

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

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

totalverbUS /ˈtoʊtəl/

add up in number or quantity

From this reading Above this we can place another layer consisting of 12 rows of 7 and 6 alternately, or a total of 78.

uspronounUS /ʌs/

the speaker and others, as the object of a verb or preposition

From this reading Thus 8 times 85 added to 7 times 78 gives us 1,226 for the full contents of the box.

wepronounUS /wiː/

the speaker together with one or more other people

From this reading On the side of the box, 14 by 22+4/5, we can arrange 13 rows containing alternately 7 and 6 balls, or 85 in all.

Chapter 21 of Amusements in Mathematics by Henry Ernest Dudeney holds 402 sentences, grouped into 81 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 21 of Amusements in Mathematics contain?

Chapter 21 holds 402 sentences of Amusements in Mathematics, unabridged, divided into 81 reading sections.

This page carries chapter 21 of Amusements in Mathematics by Henry Ernest Dudeney exactly as it stands in the source edition, without abridgement. It runs to 402 sentences, grouped into 81 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 21 of Amusements in Mathematics?

Work through the 81 sections in order, replaying any sentence and tapping unfamiliar words for their entries.

Each of the 81 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 21 be read aloud to me?

Yes — every sentence and every individual word in chapter 21 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.