Puzzle: 19 discs against 35, and one move wins
Published · By TG, the site operator
Today's puzzle uses this site's rules: 8 by 8, Black first, and a side with no legal move is skipped automatically. That matches the World Othello Federation's official rule that a player who cannot flip a disc loses the turn and the opponent moves again. The guide has the rest.
The position
A square is named by its column letter (a to h, left to right in the diagram) and row number (1 at the bottom, 8 at the top). The site's move list uses the same names in capitals; at the start they put White on d5 and e4 and Black on d4 and e5. The board can be viewed from either side, so go by the names.
8 · · ○ ○ ○ ○ ○ ○
7 · · ○ ● ● ○ · ○
6 ● ○ ○ ○ ○ ○ ● ○
5 ● ○ ○ ● ○ ● ● ○
4 ● ○ ● ○ ● ○ ○ ○
3 ● ○ ○ ● ○ ○ ○ ○
2 ● ○ ○ ○ ○ ○ · ·
1 · ● ● ● ● ● · ·
a b c d e f g h
● Black, ○ White, · empty. In words: Black has d7, e7, a6, g6, a5, d5, f5, g5, a4, c4, e4, a3, d3, a2 and b1 to f1 (19 discs). The empty squares are a8, b8, a7, b7, g7, g2, h2, a1, g1 and h1. Every other square is White (35 discs).
Black to move. Black has three legal moves: b7, g2 and g7. Only one of them wins. Which, and why?
Show the solution
g7. It flips a single disc, f7, while b7 flips seven and g2 flips eight. What matters is the other count: White's replies. In the diagram, g7 is the only square where White could play at all. Once Black takes it, White has no legal move, and the site hands the turn straight back with the message “White has no legal move. Turn passes automatically.”
The disc on g7 also closes the long diagonal. White's discs on b2, c3, d4, e5 and f6 now sit between a1 and g7, so Black plays a1 next and flips all five. White still has nothing, so Black moves a third time, a7, and leads 30 to 27. One best line from there: b7 (White), b8, a8 (White), g1, g2 (White), h2, h1 (White). The board fills and Black wins 43 to 21.
The big flips lose. After g2, White answers h2, and with best play Black loses 20 to 44. After b7, White takes g7 itself and the game ends 14 to 50; in the line the search found, Black is the one who passes, twice. After g7, a1 is also the only winning follow-up.
The idea: count replies, not flips
Near the end, ask how many places your opponent could play before you ask how many discs you turn. If it is one square and you can play it, you may move again. Every forced pass is a free move; here three moves in a row turned a 16-disc deficit into a lead.
How the answer was checked
A short script searched every continuation from the diagram to the last move, 53,156 positions, with a copy of the site's move, flip and pass rules, and agreed with the site's own engine at every position.
Try it on the site
The site has no position editor, but the habit carries over. Play the computer, and when about ten squares are empty, count the squares it could use before you choose. If there is only one, try playing it yourself, then press Undo and compare the move that flips the most. The move list shows how many discs each move turned.
Sources
- Official rules for the game Othello — World Othello Federation
Written by the operator of this site from the sources listed above. Spotted a mistake? Email warmeve.label@gmail.com and it will be corrected.