TWO RULES, THAT'S THE WHOLE GAME
A Futoshiki is a small square grid — ours is 4×4. There are only two things to know:
- Fill each row and column with 1 to 4, once each. (On a bigger grid it's 1 to 5, 1 to 6, and so on.) No repeats in a row, no repeats in a column — exactly like Sudoku, just without the little boxes.
- Obey the arrows. Some squares have a < or > between them. The arrow always points at the smaller number — the open, wide end faces the bigger one. So 3 > 1 is happy; 1 > 3 is not allowed.
That's it. The good news nobody tells beginners: those arrows aren't there to trip you up — they pin down answers a plain grid never could.
LET'S ACTUALLY SOLVE ONE — STEP BY STEP
Here's a real Futoshiki. Every square is empty except a few given numbers, and the little arrows sit between squares. Don't try to read the whole grid at once — we only ever look at one arrow at a time.
The starting grid — a few givens, arrows between some squares.
Step 1 — a chain of arrows fills a whole row at once.
Look at the top row: 1 is given, then every arrow climbs — 1 < ? < ? < ?. Four squares, each bigger than the last, using only 1, 2, 3 and 4. There's exactly one way to stack those: 1, 2, 3, 4. A whole row solved, and you've barely started. A full chain of arrows is the most generous thing on the board — always hunt for one first.
Step 2 — sometimes a single arrow is enough.
Over on the left, a given 3 sits beside an arrow opening toward the next square: 3 < ?. That square has to be bigger than 3 — and on a 4×4 the only number bigger than 3 is 4. One arrow, one answer, no scanning needed.
Step 3 — and it works at the small end too.
Same idea, flipped. Here a given 2 points at its neighbour: 2 > ?. That square must be smaller than 2 — and the only number under 2 is 1. The trick to remember: an arrow off a 3 forces a 4, an arrow into a 2 forces a 1 — the extremes give themselves away.
That's the Futoshiki-specific bit, and it's most of the early game: read the arrows, grab the forced squares, watch chains fall. Every number you drop in rules another out of its row and column — so from here it's just the no-repeats rule mopping up the last gaps:
Nearly there — only four squares left, and each is the last missing number in its row and column.
Done. Every row and column has 1 to 4 — and every arrow is happy. 👻
WHEN NO ARROW HANDS YOU ONE — TWO MORE TRICKS
Early on the arrows do plenty. When the obvious ones dry up, here are the two moves that get you going again — still no guessing.
1. Use the arrow to shrink a square's options.
An arrow doesn't always give you the exact number, but it always rules some out. A square on the small side of a < can never be the biggest value; a square on the big side of one can never be a 1. Even "this square is a 1 or a 2, nothing else" is often the clue that cracks its row. The longer the chain of arrows, the harder it squeezes.
2. Fall back on plain "what's missing?"
Underneath the arrows it's just a Latin square — every row and column needs each number once. So whenever a row or column has a single empty square, the answer is simply whichever number it's missing. Arrows get you started; the no-repeats rule finishes the squares the arrows don't reach.
So the whole loop is: find a chain and fill it, grab the forced extremes (3's and 2's next to arrows are gold), narrow the rest with "it must be one of these," and let the no-repeats rule clean up. Never a guess — every square has a reason.
THAT'S IT — GO DO ONE
Read the arrows, fill the chains, take the forced squares, let no-repeats mop up the rest. The first time a single < collapses a whole row it feels a bit like cheating, in the best way. No words, no maths homework, no ads in the middle of your puzzle — just you, the arrows, and a ghost who's quietly chuffed when you finish.