Futoshiki
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Strategy

Futoshiki Strategy & Tips

A practical strategy guide for Futoshiki: start with the extremes, trace inequality chains, use givens to bound their neighbours, and find hidden singles and pairs.

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The core idea

Bounds first, then elimination

Almost every Futoshiki deduction comes from two ideas: the inequality signs put hard bounds on what a cell can be, and the one-of-each-digit rule lets you cross candidates out along rows and columns. Learn to spot bounds fast and elimination does the rest.

  • 01

    Start with the extremes

    The largest digit N can only sit on the big side of a sign, and 1 can only sit on the small side. Any cell that must be smaller than a neighbour cannot be N; any cell that must be larger than a neighbour cannot be 1. Cross those out in your notes before anything else — on a fresh board this alone often reveals a forced 1 or N.

  • 02

    Trace inequality chains

    When signs link cells in a row, a < b < c, the cells get squeezed: a is at most N−2 and c is at least 3. A chain that spans an entire row of N cells forces the digits 1 to N in order. Even short chains cut the candidates of both ends sharply.

  • 03

    Use givens to bound their neighbours

    A given 2 with a sign saying the neighbour is smaller leaves only the digit 1. A given 4 in a 5×5 with a sign saying the neighbour is larger leaves only 5. Check every given that touches a sign before looking anywhere else.

  • 04

    Find the digit with only one home

    Pick a digit and a row. If, after crossing out, that digit fits in only one cell of the row, it goes there — even if that cell still has other candidates. Repeat for columns. This is the same hidden-single logic that drives Sudoku.

  • 05

    Work with pairs

    If two cells in a row both contain only the candidates {3, 5}, then 3 and 5 belong to those two cells in some order, and no other cell in the row can hold either. Remove them from the rest of the row. The same holds down a column.

  • 06

    Combine rows and columns

    A placement in one row removes that digit from a whole column, which can create a hidden single somewhere else. Look for cells at the crossing of a nearly-finished row and a nearly-finished column — they resolve first.

  • 07

    Let the red highlights teach you

    Rule violations turn red immediately. If you are unsure about a deduction, place the digit and see whether it lights up; if it does, undo it and you have learned something. Reserve hints for when you are truly stuck, since they cost you a best-time record.

By board size

How the approach shifts as boards grow

The habits above apply to every size. What changes is how much bookkeeping you need — see the sizes and difficulty section of the guide.

  • On small boards

    On 4×4 and 5×5 you can often solve without notes. Work outward from the givens and the extremes, and the grid falls in a few minutes.

  • On large boards

    From 7×7 upward, turn notes on from the start. Fill each empty cell with its possible digits, then repeat extremes, chains and pairs as a checklist until something breaks open.

  • When you are stuck

    Re-derive the notes for one row from scratch — a single missed elimination is the usual cause. Because every puzzle has a unique solution, a stall always means a deduction is still available.

Ready to put it into practice? Read the full how-to-play guide or jump straight in.

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