Shattering Points

Geometry Level 1

Krishna and Satvik are playing a game called 3-Point Shattering, which has the following rules:

  1. Krishna chooses where to place 3 points on a large sheet of paper.
  2. Satvik marks each point either blue or red.
  3. Krishna tries to draw a line such that all the blue points are on one side of it and all the red points are on the other.

Krishna wins if he can do Step 3. Otherwise, Satvik wins. Here are some examples of how Krishna can win:

Notice that Krishna can still win if Satvik marks all the points the same color.

Notice that Krishna can still win if Satvik marks all the points the same color.

However, if they played a slightly different game, 4-Point Shattering, where Krishna starts by placing 4 points, who has a winning strategy?

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