A pentomino is a geometric figure composed of 5 squares of the same size joined along their edges. There are 12 different pentomino shapes, if we count rotations and mirror images of a pentomino as the same. They're shown below, along with the 1-letter names that are often used for them:
Puzzle lovers have spent many hours inventing and solving dissection puzzles involving pentominoes. For example, can you cut a 6x10 rectangle into 12 pentominoes, using one of each shape? Finding even one solution by hand is difficult, but computer programs have found that there are 2339 different ways to do it. There are 1010 solutions for a 5x12 rectangle, 368 for a 4x15, and just 2 for a 3x20.
To find the coordinates of this cache, you'll need to solve an easier dissection puzzle: Cut the rectangle shown below into 8 pentominoes, so that each one contains one letter (A to H), one equal sign (=), one operation sign (+, −, x, or ÷), and two numbers. I'm not specifying which pentominoes to use, or even that they all have to be different.
Then, for each pentomino in your dissection, use the symbols in it to write an equation of the form
letter = number operation number
and use those to figure out the values of A through H. Each value should be a single digit from 0 to 9, so if your equation doesn't produce a digit, try swapping the two numbers. For example, suppose that your dissection includes this X-pentomino:
Then you could write either D=4−8 or D=8−4. The first equation gives a negative value, so you'd use the second equation instead, getting D=4.
The cache is at N 40° 5A.BCD W 124° 0E.FGH
It's a small SnapWare container, about 2 by 4 by 6 inches.
If you think you've figured out the coordinates, you can check them with certitude:
You can also see who else has solved the puzzle. Note: You can remain anonymous if you want to; incorrect guesses are always anonymous. (Puzzle makers, you can create your own certitude links here.)
Congratulations to the first certified solver and first finder, Hidegoseek.