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
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 walks one square south and one square east from its 8 and writes 9. The 9 looks north, east, west and south all at once: north and east run to the edge of the field, west stops at the first number that way, a red 15, and south at black's own 7.81615671417816159671417
Your new number looks North-East-West-South.
Red walks four squares from its 6 and writes 7. The 7 looks every way at once and sees a black 14 and its own red 4 — 7 and 14 both share 7, and the line to the 14 turns green. That 7 is rubbed out, and red walks from its 6 to the far corner instead. The 7 there looks west to the edge and south to a black 16 — 7 and 16 share nothing, the line turns red, and writing there loses.51514641651571464167515146416
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

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