XXI Strategy: How to Find the Long Path to 21
The three-tile answer in XXI is usually a 9 next to an 8 next to a 4 — the eye goes straight to it. The eight-tile answer is built out of 1s, 2s and 3s, and nobody's eye goes there without being told. These are the habits that send it there.
1. Hunt the small numbers first
A path of eight tiles averages under 3 per tile. That arithmetic alone tells you where the long answer lives: it is made almost entirely of 1s, 2s and 3s, with maybe one 4 or 5 to close. So before you drag anything, find every 1 and 2 on the grid and look at how they connect. If three or four of them are chained together along an edge or around a corner, that chain is the spine of your long path. Start there, not at the 9.
2. Work the edges and corners
Corner tiles have two neighbours and edge tiles have three, which makes them easy to run along without accidentally cutting yourself off. Long paths tend to hug the border of the grid for exactly this reason: you can sweep along the bottom row, turn up the side, and still have the whole interior available for the finish. Starting in the middle, by contrast, means every move closes off options behind you.
3. Count what's left, not what you have
The running total tells you how far you have come. The number that matters is 21 minus that — how far you still have to go — and whether the tiles still reachable from where you are can make it. If you are sitting on 16 and your only free neighbours are 6, 8 and 9, the path is dead no matter how long it is; lift and reroute. If you are on 16 and a 2 and a 3 are reachable, you have a 21 in two more moves. Get in the habit of glancing at the remainder after every tile.
4. Close with one big number
The cleanest long paths are a string of small numbers that end on a single mid-sized one. Six tiles of 1s, 2s and 3s might land you on 14, and a 7 sitting next to the last tile finishes the job in one move. Plan for that: as you build along the small numbers, keep an eye on which 5s, 6s and 7s are adjacent to your route, because one of them is probably your final tile.
5. Try the mirror
If you found a seven-tile answer and suspect there is an eight, do not keep tweaking the same route — reverse it. Start from the tile you ended on and walk the small numbers in the other direction. Reversing often reveals a different branch at the far end that was invisible from the original starting point, and in practice this is where most 7-to-8 upgrades come from.
Putting it together
On the homepage grid, the small numbers cluster along the bottom row and up the third column: 1, 2, 3 on the bottom, a 1 and a 4 above them, then 3, 5 and 2 heading up and right. That is an edge-hugging chain of small values with a natural finish — exactly what the first two habits say to look for. Running it adds up to 1, 3, 6, 7, 11, 14, 19, 21: eight tiles, with the 2 in the top-right corner closing it.
Three-tile 21s will keep finding you. The long ones you have to go looking for, and this is where to look. If you are new to the game, the full rules and a worked first grid are here.
Questions
What is the longest possible XXI path?
On a 4×4 grid of digits 1–9 the practical ceiling is around nine or ten tiles, because the smallest nine tiles on most grids already add up past 21. Most daily grids are built so that the best answer is between seven and nine tiles.
Is there always more than one answer?
Yes. Every daily grid is generated so that at least one short path and at least one long path exist. There are usually several of each, which is why two people can both score 7 with completely different shapes.
Should I start from the big numbers or the small ones?
Small ones. A long path has to be made of small numbers, so the 1s and 2s are where it lives. Big numbers are useful at the very end of a path, to close the last gap to 21 in one move.