Henry Ernest Dudeney/Modern Puzzles/81 - Pussy and the Mouse
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Modern Puzzles by Henry Ernest Dudeney: $81$
- Pussy and the Mouse
- "There's a mouse in one of these barrels," said the dog.
- "Which barrel?" asked the cat.
- "Why, the five hundredth barrel."
- "What do you mean, the five hundredth? There are only five barrels in all."
- "It's the five hundredth if you count backwards and forwards this way."
- And the dog explained that if you count like this:
1 2 3 4 5 9 8 7 6 10 11 12 13
- so that the seventh barrel would be the one marked $3$ and the twelfth barrel the one numbered $4$.
The story goes on laboriously to its inevitable conclusion that the mouse escapes before the cat has finished counting, until:
- Now, which was the five hundredth barrel?
- Can you find a quick way of arriving at the answer without making the actual count?
Click here for solution
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $81$. -- Pussy and the Mouse
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $164$. Pussy and the Mouse