Henry Ernest Dudeney/Puzzles and Curious Problems/161 - Blocks and Squares

Puzzles and Curious Problems by Henry Ernest Dudeney: $161$

Blocks and Squares

Here is a curious but not easy puzzle that appeared, we believe, some ten years ago, though the author is not traced.

Three children each possess a box containing similar cubic blocks, the same number of blocks in every box.

The first girl was able, using all her blocks, to make a hollow square, as indicated by $A$.

The second girl made a still larger square, as $B$.

The third girl made a still larger square, as $C$ but had four blocks left over for the corners, as shown.

What is the smallest number of blocks that each box could have contained?

The diagram must not be taken to truly represent the proportion of the various squares.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $161$. -- Blocks and Squares
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $229$. Blocks and Squares