GridWits
Easy tier Technique 3 of 20 Used by Smart Hint

Inequality Bound

Across a sign, the smaller cell can't reach the larger cell's biggest candidate, and the larger cell can't drop to the smaller cell's smallest.

How it works

  1. 1Both signs point left, so the three cells climb: first < second < third.
  2. 2Take the middle sign first. The third cell can be at most 4, so the second must be at most 3; the first must be at least 1, so the second must be at least 2.
  3. 3Now feed that back. The second cell tops out at 3, so the first tops out at 2; the second starts at 2, so the third starts at 3.
  4. 4Read the run as a whole and the same answer falls out in one go: three cells climbing need three different values in order, so the first can only be 1 or 2, the second only 2 or 3, and the third only 3 or 4.
  5. 5This is the move you will make more than any other. There is no separate “chain” technique to learn — applying this one sign at a time, over and over, gets you exactly the same bounds a whole-chain reading would.
1 2 3 4 1 2 3 4 1 2 3 4 < <
  • Candidates this technique rules out
  • Smaller → larger — The arrow follows the direction imposed by the inequality sign.
  • Cells read together — The connecting line shows which cells combine to make the deduction.
  • Conclusion — The coloured candidate, or the final arrow when it lands outside the pattern, shows the result.
Next in the ladder Compound Comparison →

A cell below several different cells in its own row or column must leave enough larger values for all of them; the same counting works above several cells.