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Amusements in Mathematics
Amusements in Mathematics

Chapter XIX · Chapter 19

Chapter 19 of Amusements in Mathematics is here in full — 419 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
290.--BOARDS WITH AN ODD NUMBER OF SQUARES.
There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.
Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.
At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.
Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.
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Archivist
/ˈɑːrkɪvɪst/
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A keeper or guardian of historical records and memories.

Amusements in Mathematics

Chapter XIX · Chapter 19

Chapter 19 of Amusements in Mathematics is here in full — 419 sentences across 84 reading sections, with audio for every sentence and word.

Reading 1/83 · 5 reading units · Lines 1–5

Line 1
290.--BOARDS WITH AN ODD NUMBER OF SQUARES.
Line 2
There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.
Line 3
Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.
/ˌlɪmɪˈteɪʃənz ʌv speɪs wɪl nɑːt əˈlaʊ miː tuː ɡɪv ˈdaɪəɡræmz ʌv ɔːl ðiːz bʌt aɪ wɪl eˈneɪbəl ðə ˈriːdər tuː drɔː ðem ɔːl aʊt fɔːr hɪmˈself wɪˈθaʊt ðə ˈslaɪtəst ˈdɪfəkəlti/
Line 4
At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.
/æt ˌwʌˈtevər pɔɪnt ɑːn ðə edʒ jɔːr kʌt ˈentərz ɪt mʌst ˈɔːlweɪz end æt ə pɔɪnt ɑːn ðə edʒ ɪɡˈzæktli ˈɑːpəzət ɪn ə laɪn θruː ðə ˈsentər ʌv ðə skwer/
Line 5
Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

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.

boards noun US /bɔːrdz/

(used in the plural) the stage of a theater

From this reading “290.--BOARDS WITH AN ODD NUMBER OF SQUARES.”

central adjective US /ˈsentrəl/

serving as an essential component

From this reading “There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.”

diagrams noun US /ˈdaɪəɡræmz/

plural of “diagram” — a drawing intended to explain how something works; a drawing showing the relation between the parts

From this reading “Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.”

enable verb US /eˈneɪbəl/

render capable or able for some task

From this reading “Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.”

enters verb US /ˈentərz/

third-person singular of “enter” — to come or go into

From this reading “At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.”

Fig noun US /fɪɡ/

a diagram or picture illustrating textual material

From this reading “Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.”

Limitations noun US /ˌlɪmɪˈteɪʃənz/

plural of “limitation” — a principle that limits the extent of something

From this reading “Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.”

squares noun US /skwerz/

plural of “square” — (geometry) a plane rectangle with four equal sides and four right angles; a four-sided regular polygon

From this reading “290.--BOARDS WITH AN ODD NUMBER OF SQUARES.”

All words in this reading · 80

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 Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

290

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

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

5

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

adeterminerUS /ə/

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

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 Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

allowverbUS /əˈlaʊ/

make it possible through a specific action or lack of action for something to happen

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

alwaysadverbUS /ˈɔːlweɪz/

at all times; all the time and on every occasion

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

ANdeterminerUS /æn/

the form of “a” used before a word that begins with a vowel sound

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

andconjunctionUS /ənd/

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

areauxiliary verbUS /ɑːr/

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

AtprepositionUS /æt/

in or near a particular place or position

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

boardnounUS /bɔːrd/

a committee having supervisory powers

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

BOARDSnounUS /bɔːrdz/

(used in the plural) the stage of a theater

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

bottomnounUS /ˈbɑːtəm/

the lower side of anything

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

butconjunctionUS /bʌt/

used to introduce something that contrasts with what came before

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

centraladjectiveUS /ˈsentrəl/

serving as an essential component

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

centrenounUS /ˈsentər/

a low-lying region in central France

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

cutverbUS /kʌt/

separate with or as if with an instrument

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

cuttingnounUS /ˈkʌtɪŋ/

the activity of selecting the scenes to be shown and putting them together to create a film

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

diagramsnounUS /ˈdaɪəɡræmz/

plural of “diagram” — a drawing intended to explain how something works; a drawing showing the relation between the parts

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

differentadjectiveUS /ˈdɪfərənt/

unlike in nature or quality or form or degree

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

difficultynounUS /ˈdɪfəkəlti/

an effort that is inconvenient

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

drawverbUS /drɔː/

cause to move by pulling

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

edgenounUS /edʒ/

the boundary of a surface

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

enableverbUS /eˈneɪbəl/

render capable or able for some task

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

endnounUS /end/

either extremity of something that has length

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

enterverbUS /ˈentər/

to come or go into

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

entersverbUS /ˈentərz/

third-person singular of “enter” — to come or go into

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

exactlyadverbUS /ɪɡˈzæktli/

indicating exactness or preciseness

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

fifteennounUS /fɪfˈtiːn/

the cardinal number that is the sum of fourteen and one

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

FignounUS /fɪɡ/

a diagram or picture illustrating textual material

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

forprepositionUS /fɔːr/

intended to be given to, or used by, somebody

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

giveverbUS /ɡɪv/

cause to have, in the abstract sense or physical sense

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

himselfpronounUS /hɪmˈself/

used when the man or boy doing the action is also its object

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

IpronounUS /aɪ/

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

ifconjunctionUS /ɪf/

on condition that; in the event that

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

inprepositionUS /ɪn/

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

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

intoprepositionUS /ˈɪntuː/

moving to the inside of something

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

itpronounUS /ɪt/

a thing, animal, or idea already mentioned

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

leaveverbUS /liːv/

go away from a place

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

LimitationsnounUS /ˌlɪmɪˈteɪʃənz/

plural of “limitation” — a principle that limits the extent of something

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

linenounUS /laɪn/

a formation of people or things one beside another

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

mepronounUS /miː/

the person speaking, as the object of a verb or preposition

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

mustmodal verbUS /mʌst/

used to say something is necessary, or almost certainly true

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

notadverbUS /nɑːt/

used to make a word, phrase, or sentence negative

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

NUMBERnounUS /ˈnʌmbər/

the property possessed by a sum or total or indefinite quantity of units or individuals

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

ODDadjectiveUS /ɑːd/

not divisible by two

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

OFprepositionUS /ʌv/

belonging to, or connected with, somebody or something

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

onprepositionUS /ɑːn/

touching and supported by a surface

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

oppositeadjectiveUS /ˈɑːpəzət/

being directly across from each other; facing

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

outadjectiveUS /aʊt/

not allowed to continue to bat or run

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

piecesnounUS /ˈpiːsəz/

plural of “piece” — a separate part of a whole

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

pointnounUS /pɔɪnt/

a geometric element that has position but no extension

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

readernounUS /ˈriːdər/

a person who enjoys reading

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

removedadjectiveUS /riˈmuːvd/

separated in relationship by a given degree of descent

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

sameadjectiveUS /seɪm/

Identical; not different.

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

seeverbUS /siː/

perceive by sight or have the power to perceive by sight

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

shapenounUS /ʃeɪp/

any spatial attributes (especially as defined by outline)

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

sizenounUS /saɪz/

the physical magnitude of something (how big it is)

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

slightestadjectiveUS /ˈslaɪtəst/

superlative of “slight” — (quantifier used with mass nouns) small in quantity or degree; not much or almost none or (with “a”) at least some

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

spacenounUS /speɪs/

the unlimited expanse in which everything is located

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

squareverbUS /skwer/

make square

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

SQUARESnounUS /skwerz/

plural of “square” — (geometry) a plane rectangle with four equal sides and four right angles; a four-sided regular polygon

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

thedeterminerUS /ðə/

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

thempronounUS /ðem/

the people or things already mentioned, as the object

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

ThereadverbUS /ðer/

in or at that place or location

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

thesedeterminerUS /ðiːz/

the plural of “this”: the people or things near, or just mentioned

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

throughprepositionUS /θruː/

from one end or side of something to the other

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

ThusadverbUS /ðʌs/

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

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

toparticleUS /tuː/

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

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

topnounUS /tɑːp/

the upper part of anything

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

twonounUS /tuː/

the cardinal number that is the sum of one and one or a numeral representing this number

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

waysnounUS /weɪz/

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

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

whateverdeterminerUS /ˌwʌˈtevər/

any or all of a kind, it does not matter which

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

willmodal verbUS /wɪl/

used to talk about the future, or about willingness

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

WITHprepositionUS /wɪð/

in the company of; together with

From this reading 290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

withoutprepositionUS /wɪˈθaʊt/

not having, not using, or not accompanied by

From this reading Limitations of space will not allow me to give diagrams of all these, but I will enable the reader to draw them all out for himself without the slightest difficulty.

xnounUS /eks/

the cardinal number that is the sum of nine and one; the base of the decimal system

From this reading There are fifteen different ways of cutting the 5 x 5 board (with the central square removed) into two pieces of the same size and shape.

youpronounUS /juː/

the person or people being spoken to

From this reading Thus, if you enter at point 1 (see Fig. 1) at the top, you must leave at point 1 at the bottom.

yourdeterminerUS /jɔːr/

belonging to the person or people being spoken to

From this reading At whatever point on the edge your cut enters, it must always end at a point on the edge, exactly opposite in a line through the centre of the square.

Chapter 19 of Amusements in Mathematics by Henry Ernest Dudeney holds 419 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 19 of Amusements in Mathematics contain?

Chapter 19 holds 419 sentences of Amusements in Mathematics, unabridged, divided into 84 reading sections.

This page carries chapter 19 of Amusements in Mathematics by Henry Ernest Dudeney exactly as it stands in the source edition, without abridgement. It runs to 419 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 19 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.

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Yes — every sentence and every individual word in chapter 19 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.

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

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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.