# User contributions for Prime.mover

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- 18:15, 2 December 2021
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**−2,098** Henry Ernest Dudeney/Modern Puzzles/26 - What is the Time current - 18:15, 2 December 2021
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**+2,601** N Henry Ernest Dudeney/Modern Puzzles/26 - What is the Time/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $26$ == ;What is the Time? {{:Henry Ernest Dudeney/Modern Puzzles/26 - What is the Time}} == Solution == == Proof == The minute hand by definition moves $1$ minute point per minute. The hour hand moves $5$ minute points per $60$ Definiti..." current - 18:14, 2 December 2021
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**−2,543** Henry Ernest Dudeney/Modern Puzzles/25 - A Dreamland Clock current - 18:13, 2 December 2021
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**+3,040** N Henry Ernest Dudeney/Modern Puzzles/25 - A Dreamland Clock/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $25$ == ;A Dreamland Clock {{:Henry Ernest Dudeney/Modern Puzzles/25 - A Dreamland Clock}} == Solution == :$36 \tfrac {12} {13}$ minutes after $4$. == Proof == We have that: :the minute hand takes $1$ hour to go $360 \degrees$ around the dial Definition:Anticlockwise|antic..." current - 18:11, 2 December 2021
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**−837** Henry Ernest Dudeney/Modern Puzzles/24 - Simple Arithmetic current - 18:11, 2 December 2021
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**+1,533** N Henry Ernest Dudeney/Modern Puzzles/24 - Simple Arithmetic/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $24$ == ;Simple Arithmetic {{:Henry Ernest Dudeney/Modern Puzzles/24 - Simple Arithmetic}} Note that the above is a contemporary paraphrase of the original statement of this problem, which used language and concepts which are likely to cause offence in today's society. == Solution == :$20$ and $64$. == Proof == Let their ages be $a$ and $b$. Then: {{begin-eqn}} {{eqn | l..." current - 17:36, 2 December 2021
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**−1,479** Henry Ernest Dudeney/Modern Puzzles/23 - De Morgan and Another current - 17:36, 2 December 2021
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**+2,002** N Henry Ernest Dudeney/Modern Puzzles/23 - De Morgan and Another/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $23$ == ;De Morgan and Another {{:Henry Ernest Dudeney/Modern Puzzles/23 - De Morgan and Another}} == Solution == {{AuthorRef|Augustus De Morgan}} was born in $1806$. Jasper Jenkins was born in $1860$. == Proof == Note that {{AuthorRef|Henry Ernest Dudeney|Dudeney}} was writing this in the $1920$s. The square numbers around the $18$th and $19$th..." current - 17:35, 2 December 2021
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**−3,484** Henry Ernest Dudeney/Modern Puzzles/22 - Mrs. Wilson's Family current - 17:35, 2 December 2021
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**+3,998** N Henry Ernest Dudeney/Modern Puzzles/22 - Mrs. Wilson's Family/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $22$ == ;Mrs. Wilson's Family {{:Henry Ernest Dudeney/Modern Puzzles/22 - Mrs. Wilson's Family}} == Solution == :Edgar is $21$ :James and John are both $18$ (they are twins) :Ethel is $12$ :Daisy is $9$ :Mrs. Wilson herself is $39$. == Proof == The wording is not completely clear, but it is assumed that "now" is the same time as "ten years more have passed". So, let us defi..." current - 17:34, 2 December 2021
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**−1,100** Henry Ernest Dudeney/Modern Puzzles/21 - Their Ages current - 17:34, 2 December 2021
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**+1,593** N Henry Ernest Dudeney/Modern Puzzles/21 - Their Ages/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $21$ == ;Their Ages {{:Henry Ernest Dudeney/Modern Puzzles/21 - Their Ages}} == Solution == Tom is $7$ and Mary is $13$. == Proof == Let $T$ be the age of Tom and $M$ be the age of Mary. Expressing one variable in terms of another and eliminating one of them results in a quartic: {{begin-eqn}} {{eqn | l = T^2 + M | r = 62 | c = }..." current - 17:33, 2 December 2021
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**−1,372** Henry Ernest Dudeney/Modern Puzzles/20 - The Seven Applewomen current - 17:32, 2 December 2021
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**+1,875** N Henry Ernest Dudeney/Modern Puzzles/20 - The Seven Applewomen/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $20$ == ;The Seven Applewomen {{:Henry Ernest Dudeney/Modern Puzzles/20 - The Seven Applewomen}} == Solution == Each woman sold her apples at: :$7$ for $1 \oldpence$ :$3 \oldpence$ for the odd ones left over. Thus each received the same amount:: :$1 \shillings 8 \oldpence$ As {{AuthorRef|Henry Ernest Dudeney}} put it: :''Without questioning the ingenuity of the thing, I have..." current - 17:30, 2 December 2021 diff hist +1 m Henry Ernest Dudeney/Modern Puzzles/19 - Market Transactions/Solution current
- 17:30, 2 December 2021 diff hist −156 Henry Ernest Dudeney/Modern Puzzles/19 - Market Transactions/Solution
- 17:30, 2 December 2021
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**−1,732** Henry Ernest Dudeney/Modern Puzzles/19 - Market Transactions current - 17:29, 2 December 2021
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**+2,394** N Henry Ernest Dudeney/Modern Puzzles/19 - Market Transactions/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $19$ == ;Market Transactions {{:Henry Ernest Dudeney/Modern Puzzles/19 - Market Transactions}} :''Most people will solve this, if they succeed at all, by more or less laborious trial,'' :''but there are several direct ways of getting the solution.'' == Solution == :$19$ cows, $1$ sheep and $80$ rabbits. == Proof == Recall: :$1$ pound sterling ($..." - 17:28, 2 December 2021
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**−948** Henry Ernest Dudeney/Modern Puzzles/18 - A Curious Paradox current - 17:27, 2 December 2021
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**+1,448** N Henry Ernest Dudeney/Modern Puzzles/18 - A Curious Paradox/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $18$ == ;A Curious Paradox {{:Henry Ernest Dudeney/Modern Puzzles/18 - A Curious Paradox}} == Solution == First guess: the small amount difference spans the threshold between tax brackets, which he would have had to pay to the government. == Proof == {{AuthorRef|Henry Ernest Dudeney|Dudeney}} explains it in some detail, the gist of which is as follows: A payment of $\pounds..." current - 17:26, 2 December 2021
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**−1,444** Henry Ernest Dudeney/Modern Puzzles/17 - Name their Wives current - 17:26, 2 December 2021
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**+1,939** N Henry Ernest Dudeney/Modern Puzzles/17 - Name their Wives/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $17$ == ;Name their Wives {{:Henry Ernest Dudeney/Modern Puzzles/17 - Name their Wives}} == Solution == :Catherine is Mrs. John Smith :Jane is Mrs. Henry Snooks :Mary is Mrs. Tom Crowe. == Proof == Let $C$, $M$ and $J$ be the sizes of legacies of Catherine, Mary and Jane respectively. We are given that: {{begin-eqn}} {{eqn | l = J | r = 10 + C | c = }} {{eqn |..." current - 17:25, 2 December 2021
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**−806** Henry Ernest Dudeney/Modern Puzzles/16 - Digging a Ditch current - 17:24, 2 December 2021
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**+1,291** N Henry Ernest Dudeney/Modern Puzzles/16 - Digging a Ditch/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $16$ == ;Digging a Ditch {{:Henry Ernest Dudeney/Modern Puzzles/16 - Digging a Ditch}} == Solution == == Proof == Let $r$ denote the ratio of the ability of Abraham to work relative to Benjamin. Suppose: :$A$ can dig all in $d_a$ hours and shovel all in $s_a$ hours. :$B$ can dig all in $d_b$ hours and shovel all in $s..." current - 12:10, 2 December 2021
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**−787** Henry Ernest Dudeney/Modern Puzzles/15 - Sawing Logs current - 12:10, 2 December 2021
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**+1,266** N Henry Ernest Dudeney/Modern Puzzles/15 - Sawing Logs/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $15$ == ;Sawing Logs {{:Henry Ernest Dudeney/Modern Puzzles/15 - Sawing Logs}} == Solution == $50$ shillings. == Proof == The workman charges for the number of cuts per log. A '''cord''' is a unit of volume. $4$ cords of $6$-foot logs..." current - 12:09, 2 December 2021
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**−9,971** Henry Ernest Dudeney/Modern Puzzles/14 - An Easy Settlement Replaced content with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $14$ == ;An Easy Settlement <onlyinclude> :''Three men, Andrews, Baker and Carey, sat down to play at some game.'' :''When they put their money on the table it was found that they each possessed $2$ coins only, making altogether $\pounds 1 \ 4 \shillings 6 \oldpence$.'' :''At the end of play Andrews had lost $5$ shillings and Carey had lost Definition..." current Tag: Replaced - 12:08, 2 December 2021
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**+10,463** N Henry Ernest Dudeney/Modern Puzzles/14 - An Easy Settlement/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $14$ == ;An Easy Settlement {{:Henry Ernest Dudeney/Modern Puzzles/14 - An Easy Settlement}} == Solution == There is not enough information to determine the answer uniquely. This is the solution provided by {{AuthorRef|Henry Ernest Dudeney|Dudeney}}: :''At the start of play'' ::''Andrews held a half-sovereign and a shilling..." current - 12:07, 2 December 2021
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**−10,987** Henry Ernest Dudeney/Modern Puzzles/13 - Find the Coins current - 12:06, 2 December 2021
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**+11,472** N Henry Ernest Dudeney/Modern Puzzles/13 - Find the Coins/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $13$ == ;Find the Coins {{:Henry Ernest Dudeney/Modern Puzzles/13 - Find the Coins}} == Solution == Abel: :$2$ crowns :$2$ half crowns :$1$ shilling :$1$ threepenny piece Best: :$1$ crown :$3$ shillings :$3$ Definition:Threepenny..." current - 12:02, 2 December 2021 diff hist +10 m Henry Ernest Dudeney/Modern Puzzles/47 - The Runner's Refreshment/Solution current
- 12:01, 2 December 2021
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**−3,931** Henry Ernest Dudeney/Modern Puzzles/12 - A Weird Game current - 12:01, 2 December 2021
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**+4,414** N Henry Ernest Dudeney/Modern Puzzles/12 - A Weird Game/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $12$ == ;A Weird Game {{:Henry Ernest Dudeney/Modern Puzzles/12 - A Weird Game}} == Solution == :$A$ had $9 \shillings 4 \tfrac 1 4 \oldpence$ :$B$ had $4 \shillings 8 \tfrac 1 4 \oldpence$ :$C$ had $2 \shillings 4 \tfrac 1 4 \oldpence$ :$D$ had $1 \shillings 2 \tfrac 1 4 \oldpence$ :$E$ had $7 \tfrac 1 4 \oldpence$ :$F$ had $3 \tfrac 3 4 \oldpence$ :$G$ had $2 \oldpence$..." current - 12:00, 2 December 2021 diff hist −333 Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker current
- 12:00, 2 December 2021 diff hist −29 m Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker/Solution current
- 11:59, 2 December 2021
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**+864** N Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $11$ == ;The Perplexed Banker {{:Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker}} == Solution == For $n = 1$ to $9$, put $2^{n - 1}$ sovereigns in bag $n$. Put the remaining $489$ in bag $10$. == Proof == A thinly-disguised implementation of the Basis Representation Theorem for binary. {{qed}} == So..." - 11:59, 2 December 2021
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**−525** Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour current - 11:58, 2 December 2021 diff hist −1 m Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour/Solution current
- 11:58, 2 December 2021
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**+1,025** N Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $10$ == ;Unrewarded Labour {{:Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour/}} == Solution == $16 \tfrac 2 3$ days. == Proof == Let $d$ be the number of days Willie worked. We have: {{begin-eqn}} {{eqn | l = 8 d | r = 10 \paren {30 - d} | c = }} {{eqn | ll= \leadsto | l = 18 d | r = 300 | c =..." - 11:57, 2 December 2021 diff hist −390 Henry Ernest Dudeney/Modern Puzzles/9 - Fractional Value current
- 11:57, 2 December 2021
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**+875** N Henry Ernest Dudeney/Modern Puzzles/9 - Fractional Value/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $9$ == ;Fractional Value {{:Henry Ernest Dudeney/Modern Puzzles/9 - Fractional Value}} == Solution == Two-ninths of threepence. == Proof == :$\dfrac 1 3 \times 2 = \dfrac 2 3$ So $\dfrac 1 3$ of $2 \oldpence$ is $\dfrac 2 3$ of a penny. Then: :$\dfrac 2 3$ of a penny is $\dfrac 2 3$ of $\dfrac 1 3$ of $3 \oldpence$ That is:..." current - 11:56, 2 December 2021
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**−3,178** Henry Ernest Dudeney/Modern Puzzles/8 - Buying Buns current - 11:56, 2 December 2021 diff hist −8 m Henry Ernest Dudeney/Modern Puzzles/8 - Buying Buns/Solution current
- 11:55, 2 December 2021
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**+3,655** N Henry Ernest Dudeney/Modern Puzzles/8 - Buying Buns/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $8$ == ;Buying Buns {{:Henry Ernest Dudeney/Modern Puzzles/8 - Buying Buns}} == Solution == The solution given by {{AuthorRef|Henry Ernest Dudeney|Dudeney}} is: :''There must have been three boys and three girls,'' ::''each of whom received two buns at three a penny'' ::''and one bun at two a penny,'' ::''the cost of which would be exactly sevenpence.'' However, there are in..." - 11:54, 2 December 2021
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**−2,637** Henry Ernest Dudeney/Modern Puzzles/7 - Selling Eggs current - 11:53, 2 December 2021
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**+3,106** N Henry Ernest Dudeney/Modern Puzzles/7 - Selling Eggs/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $7$ == ;Selling Eggs {{:Henry Ernest Dudeney/Modern Puzzles/7 - Selling Eggs}} == Solution == She came to market on the first day with $103$ eggs, and sold $60$ every day. == Proof == Let $n$ be the original number of eggs taken to market. Let $d$ be the number of eggs sold each day. Let $r_1$, $r_2$, $r_3$ and $r_4$ be the remaining eggs after days $1$, $2$, $3$ and $4$...." current - 11:52, 2 December 2021 diff hist +1 Henry Ernest Dudeney/Modern Puzzles/3 - Dollars and Cents/Solution current
- 11:52, 2 December 2021
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**−1,883** Henry Ernest Dudeney/Modern Puzzles/6 - Generous Gifts current - 11:52, 2 December 2021
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**+2,363** N Henry Ernest Dudeney/Modern Puzzles/6 - Generous Gifts/Solution Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $6$ == ;Generous Gifts {{:Henry Ernest Dudeney/Modern Puzzles/6 - Generous Gifts}} == Solution == $20$ people each received a dole of $6$ shillings. There is a total available weekly amount of $240$ shillings. With $5$ fewer people, we have $120$ shillings divided between $15$ people, that is $8$ Defini..." current - 11:50, 2 December 2021
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**−5,504** Henry Ernest Dudeney/Modern Puzzles/5 - Doubling the Value current