Balanced Zebra

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

The Balanced Zebra board

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Grades
3–6
Subjects
Multiplying & Dividing, Shapes & Space, Logic
Kind
Puzzle
Cost
Free, no account, no ads

What it is

Zebra’s field with nobody to play against. The board arrives all black; tap a hexagon and it turns white. Hexagons of one colour that touch make a herd, and a colour is worth its herd sizes multiplied together. The two colours have to come out worth the same, which is easy, and then as large as the shape will allow, which is not.

The rules

A short chain of six black hexagons, drawn as one animal wearing the number 6. One of them is tapped and turns white, splitting the black animal in two; tapped again it turns black and they close up.62316
A zebra's pelt is striped black and white. This one starts all black. Tap a hexagon to turn it white.
A curved board of twelve hexagons: seven black in a row, drawn as one animal wearing the number 7, and five white beside them. The middle black one turns white, and the black animal becomes two, each wearing the number 3.753315
Black scores by multiplying together the sizes of all its groups. White does the same.
A ring of twelve hexagons cut in half: one black animal of 6 and one white animal of 6, which is level at 6. Then the same ring cut into four animals of 3, two black and two white — still level, and now worth 9 to each side.663333
Make the two scores equal, and as big as you can.
A ring of twelve hexagons cut into four animals of three, two black and two white, which is level. Two hexagons then change hands: the black animals are still three and three, and the white ones are four and two — one less.33333342
In the last pack, the two scores must be one apart instead.

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. Chains, loops, diamonds and triangles each break differently. The last pack changes the rule — the two colours must miss each other by exactly one, three and three against four and two — and every target printed on a board is the true best, 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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