Henry Ernest Dudeney/Puzzles and Curious Problems/329 - The Four Pennies/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $329$

The Four Pennies

Take four pennies and arrange them on the table without the assistance of another coin or any means of measurement,

so that when a fifth penny is produced it may be placed in exact contact with each of the four (without moving them)

in the manner shown in the diagram.

The shaded circle represents the fifth penny.

How should you proceed?

Solution

Arrange the pennies as follows.

Note they have been labeled from $1$ to $4$.

Move penny no. $1$ to touch $2$ and $4$:

Move penny no. $4$ to touch $2$ and $3$:

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $329$. -- The Four Pennies
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $382$. The Four Pennies