Gozen

Your next number is forced, so a prime is always coming — and on a prime only a square nobody watches will do.

The Gozen board

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Grades
4–6
Subjects
Multiplying & Dividing, Logic
Kind
Two-player game
Cost
Free, no account, no ads
Original
Gozen at MathPickle

What it is

Tomoe Gozen was a female warrior who led hundreds of Samurai into battle 800 years ago. Turns alternate. On your turn, start at your last number and move north, east, west or south up to four times, to empty squares only. On the square where you stop, write the starting number +1. Your new number then looks north, east, west and south, and if the first number it sees in any of those directions is an enemy that shares no prime factor with it, you lose. You also lose if you cannot move.

The rules

Tomoe Gozen was a female warrior who led hundreds of Samurai into battle 800 years ago.

A five-by-five field, a red 2 in a corner and a black 9 in the middle. Red walks four squares from its 2 and writes 3 where it stops; then black walks two squares from its 9 and writes 10. Each number climbs by one — only where it stands is chosen.9239239102
Turns alternate. On your turn, start at your last number. Move North-East-West-South up to 4 times to empty squares. On the square you stop, put the starting number +1.
Black writes 9 beside its own 8 and looks four ways. A dashed ray south stops at the red 15, the first number seen that way. The ray east stops at black's own 8, so the red 16 behind the 8 is not seen at all. North and west run off the field.81615671417981615671417
Your new number looks North-East-West-South.
Red must write 7. On the square red takes, the one enemy in sight is a 14 across an empty square — 7 and 14 both share 7, and the ray turns green. On the reachable far corner a 16 looks up four empty squares of column — 7 and 16 share nothing, the ray is red, and the field flinches: writing there loses.51514641651571464167
If the first number it sees in any of these directions is an enemy that does not share a common prime factor - you lose.

You also lose if you cannot move.

What it gives you to practise

Factors and primes under pressure, because the next number is always forced. Count forward and you know a prime is coming; a prime shares a factor with almost nothing, so when it arrives the only square that will do is one where nobody is watching. Your own numbers block the view and shield whatever stands behind them, so the board is as much a question about lines of sight as about arithmetic.

In a classroom

Gordon Hamilton, MathPickle. Four rivals, named for what each one can do rather than for how hard it is, and their order was measured by self-play rather than picked by eye. There is a two-player hot seat on one tablet, and an online room for when the second player is somewhere else.

Share or embed

The whole game at one address, with every board in it. Whoever opens it stays inside it, and their progress stays in their own browser.

Play Gozen

Near it on the shelf