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# 3D Treasure Hunt

*This problem follows on from Treasure Hunt, which you may wish to explore first.*

Imagine you are looking for treasure in a strange three-dimensional treasure island, where treasure can be hidden at any point on a grid defined by three coordinates.

When you enter a guess in the interactivity below, it tells you the shortest distance you would have to travel along grid lines to reach the treasure.

For example, if the treasure is at (1, 2, 3) and you enter (3, 3, 3), the interactivity will tell you that the treasure is a distance of 3 steps away (2 steps in the x direction, 1 in the y direction and 0 in the z direction).

**Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of moves?**

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Age 14 to 18

Challenge Level

Imagine you are looking for treasure in a strange three-dimensional treasure island, where treasure can be hidden at any point on a grid defined by three coordinates.

When you enter a guess in the interactivity below, it tells you the shortest distance you would have to travel along grid lines to reach the treasure.

For example, if the treasure is at (1, 2, 3) and you enter (3, 3, 3), the interactivity will tell you that the treasure is a distance of 3 steps away (2 steps in the x direction, 1 in the y direction and 0 in the z direction).