Khachaturyan A.V.

Mom baked pies - three with rice, three with cabbage, and one with cherries - and laid them out in a circle on a plate (see fig.). Then she put the plate in the microwave to warm it up. All the pies look the same. Masha knows how they were arranged, but she doesn’t know how the plate turned. She wants to eat the cherry pie, and considers the others tasteless. How can Masha definitely achieve this, biting into as few tasteless pies as possible?

![](https://cdn.mathpix.com/cropped/2024_05_06_61f459f9e45cb4d6ceb6g-10.jpg?height=352&width=352&top_left_y=1808&top_left_x=859)
It is clear that Masha cannot solve the task with just one bite. If Masha, for example, tried a cabbage-filled bun, she cannot determine which of the three she got, and therefore cannot confidently find the bun with the cherry. Let's show how Masha can solve the task in two bites. Suppose Masha bit into a bun, and it turned out to be not with cherry, but with cabbage. Then she can try the bun that is one position clockwise from it. If this is the bun with cherry, Masha has achieved her goal; if it is with rice, then the desired bun is between the bitten ones; and if it is again with cabbage, then she should take the next one clockwise, and this will definitely be the bun with cherry.

If the first bun is with rice, Masha can act similarly, but move counterclockwise.