Henry Ernest Dudeney/Modern Puzzles/79 - Egg Laying/Solution
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Modern Puzzles by Henry Ernest Dudeney: $79$
- Egg Laying
- If a hen and a half lays an egg and a half in a day and a half,
- how many and a half who lay better by half will lay half a score and a half in a week and a half?
Solution
One hen.
Proof
Half a score and a half is $10 \tfrac 1 2$.
A week and a half is $10 \tfrac 1 2$ days.
We have that $1 \tfrac 1 2$ hens lay $1 \tfrac 1 2$ eggs in $1 \tfrac 1 2$ days.
Hence $1$ hen lays $1$ egg in $1 \tfrac 1 2$ days.
A hen who lays better by half will lay $1 \tfrac 1 2$ eggs in $1 \tfrac 1 2$ days.
That is, $1$ egg in $1$ day.
Let $n + \dfrac 1 2$ be the number of better-by-half laying hens who lay $10 \tfrac 1 2$ eggs in $10 \tfrac 1 2$ days.
The same number of hens lay $1$ egg in $1$ day.
That is, half a hen and half a hen, or one hen.
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $79$. -- Egg Laying
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $161$. Egg Laying