Lonely Zebra

Both colours have to multiply out to the same number, and then to the largest that shape allows.

The Lonely Zebra board

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Grades
3–6
Subjects
Multiplying & Dividing, Shapes & Space, Logic
Kind
Puzzle

What it is

Zebra’s field with nobody to play against. Every hexagon is painted black or white. Hexagons of one colour that touch make a herd, and a colour is worth its herd sizes multiplied together. There are three ways to play: make black alone as large as possible; make the two colours worth the same, and then as large as possible; or make them differ by exactly one, and then as large as possible.

The rules

A ring of twelve hexagons painted in stripes, two black and two white. Two hexagons then change colour, and one white stripe grows while the other shrinks.
Create a Zebra pelt.
A ring of twelve hexagons in four stripes of three, two black and two white, each wearing the number 3. Two hexagons then change colour: the black stripes are still 3 and 3, and the white ones are 4 and 2.33333342
Black scores by multiplying together the sizes of all its groups. White does the same.

What it gives you to practise

The same multiplication insight as Zebra with the opponent taken away, so there is nothing to react to and nowhere to hide: every board is a question about how one fixed shape can be cut. The three ways of playing run through the same loops, diamonds and triangles, so only what the numbers have to do changes from one to the next — and two colours one apart can never be cut alike, because neighbouring numbers share no factor. The largest score each board allows was found by a computer trying every way of painting it.

In a classroom

The maximum is never printed on the board before somebody reaches it, and that is deliberate. A class can hunt for a number nobody has told them, and the board will say when they have it.

Share or embed

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

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