Juniper Green

Rules — Juniper Green

• All the numbers from 1 to N are on the table. Players take turns picking one that has not been used.
• The first number of the game must be even.
• After that, each number must be a multiple or a divisor of the previous one.
• A number can only be used once.
• Whoever cannot pick a number loses.

Levels:

• Level 1 — numbers 1 to 20.
• Level 2 — numbers 1 to 40.
• Level 3 — numbers 1 to 100.

The board highlights the numbers you are allowed to pick, so nothing illegal can be played by accident. Against the computer you also choose who starts.

Blue opens with 2 — it has to be even. Maroon answers 1, which is a divisor of 2 and, being a divisor of everything, looks like the safest number on the board. Blue then says 13, and the game is over: maroon cannot move.

Why 13 kills: its only divisor other than itself is 1, and the 1 has just been spent. Its multiples would be 26, 39, 52… and none of them fit under 20. A prime bigger than half the board is a dead end — and the player who walks into it is whoever has to answer it.

So the 1 is not the safe number it looks like: it is the key that unlocks the traps, and handing it over is handing over the win. Watch what happens to the big primes — 11, 13, 17, 19 — as a game goes on.