Kajitsu

Cutting fruit into pieces of a given size and symmetry: every morsel has to fold or spin onto itself.

The Kajitsu board

Play Kajitsu Share or embed

Grades
3–6
Subjects
Shapes & Space, Logic
Kind
Puzzle
Cost
Free, no account, no ads
Original
Kajitsu at MathPickle

What it is

Kajitsu is Japanese for fruit. Each fruit is a patch of hexagons with pips on it, and every pip owns one morsel. The number on a pip says how many hexagons its morsel takes. The mark beside it says what symmetry that morsel must have: a double arrow to fold across a line, curved arrows to turn onto itself, as many times round as there are arrows.

The rules

Kajitsu is Japanese for fruit. Cut each one into morsels — one for every pip.

A finger drags across three hexagons to make one morsel for the pip marked 3, then across three more for the other pip, and the fruit is cut up.3333
Tap a pip, then drag: the number on it says how many hexagons its morsel takes.
The pip marked 5 carries a double arrow and a dashed fold line. A hexagon on one side of the line is ringed together with its mirror on the other, and both are taken; then another pair.52
A double arrow means the morsel folds across the dashed line, so a hexagon and its mirror are both in it.
The pip carries three curved arrows. A hexagon is ringed together with the two it turns onto, all three are taken, and the finished morsel turns a third of a circle onto itself twice over.6
Curved arrows turn the morsel onto itself instead — as many times round as there are arrows.

What it gives you to practise

Symmetry as a property you have to build rather than recognise. A shape that folds across a line is a different demand from a shape that turns onto itself three times, and on a hexagonal grid neither one sits where intuition trained on squares expects. The cut also has to tile: every hexagon belongs to exactly one morsel, so a beautiful piece that strands its neighbour is no good.

In a classroom

The board prints. There is a print stylesheet that erases the answers, hides the screen controls and turns the coloured fruit into line art a pencil can reproduce, so the same board can go round a table on paper.

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.

Play Kajitsu

Near it on the shelf