Roadworks

Rules — Roadworks

• The board is a city: a grid of m×n blocks. Its corners at the bottom left and top right are A and B. Every point where streets meet is a crossing.
• You take turns. On your turn you close one crossing (never A or B, and never one already closed). A closed crossing gets a roadworks fence in your colour.
• A path goes along the streets, in any direction, and only through open crossings.
• Whoever leaves A and B with no path between them loses — the game ends at that very moment. (This is the misère version: you have to avoid making the last closure that matters.)
• Dead ends close by themselves (levels 2, 3 and 4). After every closure, any crossing that is no longer on any path from A to B falls: isolated crossings, dead-end alleys and loops hanging from a single crossing. They turn grey and nobody can use them any more. Closing one crossing can make several others fall, so count carefully!

Levels:

• Level 1 — Basic: 3×3 blocks, nothing falls.
• Level 2 — Medium: 3×3 blocks, dead ends close.
• Level 3 — Advanced: 4×4 blocks, dead ends close.
• Level 4 — Competition: 5×5 blocks, dead ends close. There is no computer at this level: it is played between students and in competitions.

Against the computer you choose who starts. Without falling crossings (level 1) the result depends only on parity: with sensible play the first player wins. When dead ends close, one closure can change the parity and a real strategy appears. A game by Georgy Nuzhdin.

On a 3×3 grid of blocks: each turn you close a crossing (here, one after another, in maroon and navy), and a roadworks fence goes up. After the second closure, a2 and a4 fall by themselves (they turn grey): a2 hangs only from A and a4 only from b4, so they are on no path from A to B. The lines that reach a closed or fallen crossing fade out, so you can see the network that is left. The last closure, b1, leaves A with no way to B — and whoever makes it loses.

Close crossings, but do not be the one who leaves A and B cut off from each other. And watch what falls!