SOLO-034 · Othello / Reversi
EXTREMEThe Defense Tree
Black plays. Find his only best first shot and the final differential that he can guarantee against any optimal defense.
Materials: Pencil, gum; tray 8 × 8 and optional reversible pions.
Rules you need
- Tray 8 × 8; columns A to H from left to right, lines 1 to 8 from top to bottom. N = Black, B = White, · = empty box.
- A shot sets a pawn on an empty box and must frame at least one opposing pawn between this pawn and a friendly pawn, in a straight horizontal, vertical or diagonal line. All frames created are turned.
- Without a legal blow, you have to pass. If no camp can play, the game stops. Score: number of his pawns less number of opposing pawns; empty boxes do not count. The goal is to maximize this differential, not just to win.
The puzzle
Trait : Black. There are 10 empty boxes left.
For the evidence, also give the best defense after your first blow, then examine the other legal blows. No second person is necessary: analyze both sides on paper.
| L / C | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| 1 | B | N | N | · | B | · | · | N |
| 2 | B | N | N | B | · | · | · | N |
| 3 | · | B | B | N | N | N | N | N |
| 4 | N | B | B | N | B | N | B | N |
| 5 | B | N | N | B | N | N | B | N |
| 6 | · | N | B | B | B | N | B | N |
| 7 | · | B | N | N | N | N | N | · |
| 8 | B | B | N | N | N | N | N | N |
Your workspace
Write down your assumptions separately from deductions you have proved.