SOLO-018 · Futoshiki
EXPERTThe Seven Staircases
Complete square 7 × 7 with figures from 1 to 7.
Materials: Pencil, gum and gridded paper; no commercial game required.
Rules you need
- Each row and column contains exactly once every 1-7 digit. There are no 3 × 3 regions and no diagonal constraints.
- The printed values are fixed. All inequalities in the list are strict and must be respected simultaneously.
- LrCc is the line r and column c, counted from the top and left. A box marked " ·" is to be filled in.
The puzzle
All useful inequalities are given below; the neighbourhoods not mentioned do not bear any additional constraints.
L5C1 < L4C1
L6C6 < L5C6
L3C6 < L3C7
L2C6 < L2C7
L6C2 < L7C2
L4C1 < L3C1
L7C7 < L7C6
L5C7 < L6C7
L5C2 < L4C2
L1C4 < L1C5
L1C4 < L2C4
L6C1 < L7C1
L6C4 < L7C4
L6C6 < L6C5
L4C2 < L3C2
L4C5 < L3C5
L2C7 < L3C7
| L / C | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | · | · | · | 2 | · | 5 | · |
| 2 | 6 | · | · | · | 4 | · | · |
| 3 | · | · | 3 | · | 5 | · | · |
| 4 | · | · | · | 6 | · | · | · |
| 5 | · | · | · | · | · | · | · |
| 6 | · | · | · | · | · | · | 7 |
| 7 | · | · | 5 | · | · | 6 | 3 |
Your workspace
Write down your assumptions separately from deductions you have proved.