Someone once said that there were only two original math puzzles – one with numbers and one with shapes – and that all others are derivations of those. Oh wait, that was me who said it. Looking through my archive of derivatives, I found a puzzle that truly melds arithmetic and geometry.
The shapes employed are the 12 pentominoes, configurations of 5 squares joined at entire sides. They are pictured below with their letter names.
Most pentomino puzzles are difficult because there are so many possible ways to assemble them, but we will begin with simple ones. For example, the V, L, and P can be arranged to form a 3x5 rectangle as shown below. Note: the pieces can be rotated and/or reflected. We show the “stick figure” version of the pieces.
We could put a number in each individual square and then each piece would have a sum. At first I thought that adding a numerical requirement would make the challenges tougher, but I was wrong. When the grid is numbered and each piece in the solution has a sum in common with the others, it helps with the assembly. Here is a sample.
Challenge 1: Use the L-pentomino and two pieces other than V and P to make the rectangle below. Each piece will have a common sum of 15.
We put the solution at the bottom of this page. Could you have figured the common sum without being told? Could you solve this type of puzzle without a physical set of pieces? If not, perhaps you can make a set out of cardboard or a manila folder. Here is a link to a printable pattern.
Here are your challenges.
For Challenge 2: What is the sum per piece? Let the numbers help you choose the pieces.
Hint for Challenge 3: Use W and Z with three other pieces.
Solution to Challenge 1 above.
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