Henry Ernest Dudeney/Puzzles and Curious Problems/243 - The Squirrel's Climb/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $243$

The Squirrel's Climb

A squirrel goes spirally up a cylindrical post, making the circuit in $4$ feet.

How many feet does it travel to the top if the post is $16$ feet high and $3$ feet in circumference?

Solution

$20$ feet.

Proof

In going $3$ feet around, the squirrel goes $4$ feet up.

These are the sides of the classic $3$-$4$-$5$ triangle.

Hence in going up $4$ feet, the squirrel travels $5$ feet.

Hence in going $16 = 4 \times 4$ feet, the squirrel travels $4 \times 5 = 20$ feet.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $243$. -- The Squirrel's Climb
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $324$. The Squirrel's Climb