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This month's question was sent in by Jan Fricke. (Thanks, Jan! More credits
will be given on the solution page.)
Consider the arithmetic sequence x, 2x, 3x,..., up to n×x, for an irrational x. If you round the numbers to the nearest integer, some of them will have been rounded up and some rounded down. Let d be the number of those rounded down and u be the number of those rounded up. For which x values is the difference |d-u| bounded as n approaches infinity, and for which is it unbounded? As usual: prove your answer. |
List of solvers:Yury Volvovskiy (13 August 23:24)Yuping Luo (17 August 22:41) Radu-Alexandru Todor (20 August 11:08) |
Elegant and original solutions can be submitted to the puzzlemaster at riddlesbrand.scso.com.
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The solution will be published at the end of the month.
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