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

Play Gozen

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’s battlefield, eight hundred years on. You and an enemy commander write climbing numbers across it. You never choose which number you write, only where it stands: march up to four squares from your largest and put the next one down. It then looks four ways and sees the first number in each direction, and every enemy number it can see must share a factor bigger than 1 with yours — or it falls.

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.

The rules

Tomoe Gozen's battlefield, eight hundred years on. You and an enemy commander write climbing numbers on it, and the numbers you write are the ones that keep you alive.

Walk up to four squares from your largest number and write the next one — you never choose the number, only where it stands.

The new number looks four ways and sees the first number in each. Your own numbers block the view and shield whatever stands behind them.

Every enemy number in sight must share a factor bigger than 1 with yours. If even one shares nothing, you fall.

Play Gozen

Near it on the shelf