
Here's a solution to the last figure shown—the long wall that's a 4x21 parallelogram. The solution is not unique. We were aiming to separate the smaller pieces. Can you get them to cluster?
Open question to the world:
Find 7 congruent figures, each 12 units in area, using the entire set. We've found two such shapes. Find another, or prove there are no others, and you'll win a nice prize.
And the answer!
After 7 years of hanging in unresolved limbo, this challenge was answered on January 2, 2019, by Randy Ekl, a game designer and software engineer from Illinois, who used both logic and a computer program to prove that the two shapes we had identified were, indeed, the only two possibilities. Here are the two shapes that you can make in 7 congruent copies each, using the entire set of Hopscotch pieces. No, we won't show you the full solution. We'll let you have the fun of working those out for yourself.
Kudos, Randy! You're a winner.
