The Kakuro book said “Expert.” You believed it for the first ten minutes, while the corners filled in nicely. Now you’re looking at a block in the middle of the grid where every clue has five ways to be right, your pencil marks are three deep, and the eraser has worn a soft gray …

You’re twenty minutes into a hard Kakuro, and you’ve just worked out 17 in two cells for the third time tonight. 9 and 8. You knew that. You also knew it the last two times, and you still ran the arithmetic, because the habit hasn’t moved from your head to your eyes yet.

That small …

You’ve hit a wall in an expert Kakuro. Every magic block on the page is filled in, every easy crossing is done, and a fat block of empty cells is sitting in the middle of the grid. Each clue around it has five or six workable combinations. You pencil a few, erase them, and pencil them again. …

You’ve spotted the 16 in the corner of a Kakuro grid. Two cells, so it’s 7 and 9. You pencil “7 9” into both cells and feel good about it for about four seconds. Then you notice the 17 next to it is “8 9” in both cells too, and the 24 below is “7 8 9” …

You’re down to the last four squares of an expert Kakuro. You try one fill and every clue checks out. You erase it, try the other, and every clue checks out again. Your pencil hovers. One of them has to be wrong, and the puzzle has stopped giving you hints.

So you pick one. If you’re …

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 …