A ladybird is free to fly between the 1 × 1 cells of a 10 × 10 square grid. She may begin in any 1 × 1 cell of the grid. Every second she flies to a different 1 × 1 cell that she has not visited before.
Find the smallest number of cells the ladybird must visit, including her starting cell, so that you can be certain that there is a 2 × 2 grid of adjacent cells, each of which she has visited.
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Cayley Mathematical Olympiad 2020 (2020)
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