Hints and Solution for "The Calibron 12-Block Puzzle"

The Calibron 12-Block Puzzle consists of 12 rectangular pieces, or blocks, that you are to arrange into a single perfect rectangle or square. Each piece is inscribed with its dimensions, to make it easier for you to analyze it and keep track of your progress while solving it.

This is not an easy puzzle. Finding the solution requires patience and a systematic approach to searching for the right arrangement; it's extremely unlikely that random fiddling with the pieces will yield success. That being said, there are some approaches to reducing the size of the search space, and this series of hints explains a few of those approaches along the way.

Of course, it's difficult to really get started on such a puzzle until you know what the actual goal is. The instructions only specify "a perfect rectangle or square", which is awfully open-ended.

Hint #1: How can we figure out what the actual goal shape is?"