Treasure Map

Chris found a treasure map. The map can be visualized as a grid of size 4 × 4 4\times 4 as shown below:

As you can see, the map is mostly faded and only the numbers 1 1 and 2 2 are visible. However, a wise man gave Chris a clue:

The shortest distance to the treasure from a cell with the shortest distance of 2 from number 2 in the grid above is 3.

How many possible locations can the treasure be buried under?

Details and Assumptions:

  • A cell is adjacent to another if it is located on either its top, bottom, left, or right.
  • An adjacent cell has a distance of 1.
6 8 5 4 7

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1 solution

  1. The blocks marked 2 in blue are all the blocks that are at distance 2 from the block marked 2 in black.

  1. all the red blocks marked 3 are at distance three from at least some block

Hence, there are 8 possible locations.

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