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

by : $161$

 * 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.


 * Dudeney-Puzzles-and-Curious-Problems-161.png


 * 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.