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--- pow:problem7s23 [2023/05/09 14:39] – mazur
+++ pow:problem7s23 [2023/05/10 03:55] (current) – mazur
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+<box 85% round orange| Problem 7 (due Monday, May 8)>
+bats live in groups occupying some of the 5050 caves in the
+Magic Mountains (where bats live forever). Every night one bat from each occupied cave flies out. The bats
+meet and play together all night. At dawn they all go to one (the same) of the
+unoccupied caves to rest.
+Show that from some point on there will be the same number of bats out
+every night.
+</box>
+This problem in a slightly different wording is known as the {\bf Bulgarian solitaire}. We received three solutions.
+Prof. Vladislav Kargin submitted a beautiful solution, much simpler than our original solution (which reduces
+the problem to our Problem 6 this semester). The solutions by Aleksandr Aksenchuk and Krishnaraj Sambath are
+incomplete and contain some interesting partial observations, like the realization that the equality
+$5050=1+2+\ldots+100$ plays important role here and that from some day on we should always have
+one cave with exactly $i$ bats for $i=1,2,\ldots, 100$. For detailed solutions see the following link {{:pow:2023sproblem7.pdf|Solution}}. See also the following link for a nice discussion of this problem
+https://www.researchgate.net/publication/273158618_The_Bulgarian_solitaire_and_the_mathematics_around_it