You’ve solved a few hundred Kakuro grids, and one evening you decide to make one. Graph paper, a pencil, an hour. You shade some black squares, write digits in the white ones, add up the sums, and hand the finished puzzle to a friend. Ten minutes later they slide it back across the table. The …

The cover says “Extreme Kakuro.” You open to a 15x15 grid and finish it in twelve minutes, because every corner has a 3 or a 17 in two cells that practically fills itself in. Two pages later there’s a little 7x7 marked “Medium.” Forty minutes in, you’re staring at …

You want a Kakuro that opens a padlock. The lock takes three digits, and the plan is simple: solve the grid, read three shaded cells, turn the dials. Then you try it. You fill the grid first, shade three cells that happen to look nice, and read off 3-8-6. The lock was set to 4-0-7 weeks ago. Your …