Your first Kakuro grid looks like a crossword someone forgot to finish. Black squares are slashed with diagonal lines, small numbers sit in their corners, and rows of empty white boxes wait for you. You pick the first clue you see, a 15 across three cells, and start trying combinations. 9, 5, 1? 8, …

You open the puzzle book to the Kakuro page, uncap the pen, and look at the first clue cell. It holds two numbers, 24 and 16, separated by a diagonal line. Which one goes with the row? You pick the 24, spend five minutes building a combination that adds up to it across two cells, and realize two …

A fresh Kakuro grid sits in front of you, every white cell empty. Your eye lands on a 27 running across five cells, so you start there. 9, 8, 6, 3, 1? 9, 7, 5, 4, 2? 8, 7, 6, 4, 2? All valid. There are eleven different digit sets that add to 27 in five cells, and nothing yet tells you which one is …

You found the 3 in the corner of your Kakuro grid. Two cells, so it’s a 1 and a 2. You penciled both digits into both cells and felt good about it. Now you’re staring at those two cells, pencil hovering, and the question is simple: which one gets the 1?

You could flip a coin. Half the …

Twenty minutes in, the grid is mostly full. You write the last digit of a long across entry, add it up to check, and come up one short. You check the down entry through that cell. It’s off too. You start tracing backward, cell by cell, and the trail keeps going. Ten minutes later you’re …

You can finish a hard Sudoku in ten minutes. You spot X-wings without trying, and naked pairs jump out at you. So you flip to the Kakuro page expecting a warm-up, and twenty minutes later you’ve placed four digits, erased three of them, and you’re refusing to write a 5 in a cell because …