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Find the Metagiff

Age 11 to 16 Challenge Level:

This resource is part of "Dotty Grids - Exploring Distance"

You may wish to try Find the Robber before exploring this problem.

In a three dimensional city on a distant planet, the metagiff has escaped from the zoo!
Can you help the sheriff locate the metagiff?

The metagiff is hiding at a point on the three dimensional grid, so his location is specified by three coordinates (x,y,z).

Choose coordinates where you think the metagiff might be hiding. The interactivity tells you the shortest distance to the metagiff, travelling along the grid lines.

Try to find the metagiff using only a few guesses.

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Can you guarantee to always find the metagiff in less than six guesses? Can you do better than this?

How would your strategy change if the metagiff were allowed to move 1 space after each guess?

Can you think of any other mathematically interesting variations of the game?