The puzzle: “There is only One Way to make a SQUARE out of these 5 pieces”

In all abstract reasonings, there is one point of view, which, if we can happily hit, we shall go farther towards illustrating the subject, than by all the eloquence and copious expression in the world. — David Hume, “An Enquiry Concerning Human Understanding”, 1748.

The image says, “There is only One Way to make a SQUARE out of these 5 pieces”.

The puzzle above took me about an hour to solve.

First, I approached it by the direct means — rearrange the pieces and try to make a square. That failed. Abysmally.

A perfect square but with one piece unused. Close but no cigar.

Next, I computed the area of the goal square by measuring the dimensions of the box in which the pieces came ((2×4)+(½×2×1)=9 sq. inches). This was much more promising because I figured which edges of the pieces would be sides of the final square and which were diagonals. Still, I couldn’t find the answer.

The box’s dimensions.

Finally, I drew a 3”×3” square on a paper and placed the pieces to fit. et voila! In 5 minutes I was done. You could say the pieces just fell into place 😉.

My 3”×3” square. Answer left out for would be puzzlers.

Whether I would’ve been as fast had I just drawn a square and attempted to fit the pieces without the earlier attempts is an open question.