Henry Ernest Dudeney/Puzzles and Curious Problems/335 - Three Times the Size

Puzzles and Curious Problems by Henry Ernest Dudeney: $335$

Three Times the Size

Lay out $20$ matches in the way shown in the diagram.

You will see that the two groups of $6$ and $14$ matches form two enclosures, so that one space is exactly $3$ times as large as the other.

Now transfer one match from the larger to the smaller group, and with the $7$ and $13$ enclose two spaces again, one exactly $3$ times as large as the other.

Twelve of the matches must remain unmoved from their present positions --

and there must be no duplicated matches or loose ends.

The dotted lines are just there to indicate the respective areas.

Also see

• $211$ - The Twenty Matches, in the same collection

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Unclassified Problems: $335$. -- Three Times the Size
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Match Puzzles: $502$. Three Times the Size