Stirring Paint

Deduction with no arithmetic in the way — colours, directions and jumps, worked out until every loop closes.

The Stirring Paint board

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Grades
2–6
Subjects
Logic
Kind
Puzzle
Original
Stirring Paint at MathPickle

What it is

Every cell needs three things: a colour, a direction and a number. The number is how far its arrow jumps, and it has to land on its own colour. When the board is right, each colour’s arrows form a single loop — follow the jumps and you come back where you started.

The rules

Fill in every cell so all the paint stirs around in loops.

Three cells of a small board are finished. The fourth is a bare grey diamond: it takes red paint, then points left, then takes the number one.11111111111
Every cell needs a colour, a direction and a number.
On a finished board, the blue arrow marked two points left. A splat of blue paint flies two cells to the left, onto the blue arrow waiting there.111112211111221111222
The number is how far it jumps. It must land on its own colour.
One colour lights up and the rest of the board fades back. Its paint jumps from arrow to arrow, one jump at a time, round from the first to the last and back to the first.111112211112221111122
Each colour's arrows make one loop. Follow the jumps and you come back where you started.

What it gives you to practise

Deduction with the arithmetic moved out of the way. Nothing on this board has to be calculated; things have to be ruled out. A cell whose jump would land off the edge is decided for you. A colour that has already closed its loop cannot take another arrow. Some boards carry spare paints, which means they are genuinely ambiguous — there is no stored answer to match, only rules that a filled-in board either satisfies or does not.

In a classroom

Gordon Hamilton, MathPickle. It suits a class with a wide spread of arithmetic fluency better than most boards do, because none of the difficulty in it is arithmetic — a child who is behind on tables is not behind here.

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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