Henry Ernest Dudeney/Modern Puzzles/15 - Sawing Logs/Solution
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Modern Puzzles by Henry Ernest Dudeney: $15$
- Sawing Logs
- "Your charge," said Mr. Grigsby, "was $30$ shillings for sawing up $3$ cords of wood made up of logs $3$ feet long,
- each log to be cut into pieces $1$ foot in length."
- "That is so," the man replied.
- "Well, here are $4$ cords of logs, all of the same thickness as before,
- What will your charge be for cutting them all up into similar $1$-foot lengths?"
- It is curious that they could not at once agree as to the fair price for the job.
- What does the reader think the charge ought to be?
Solution
$50$ shillings.
Proof
The workman charges for the number of cuts per log.
$4$ cords of $6$-foot logs is the same number of logs as $2$ cords of $3$-foot logs.
The key point is that:
but:
So the workman should charge:
- $30 \times \dfrac 2 3 \times \dfrac 5 2 = 50 \shillings$
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $15$. -- Sawing Logs