EPT[Math Puzzle] Day12 - Page 2
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King K. Rool
Canada4408 Posts
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mmp
United States2130 Posts
+ Show Spoiler + Let a row contain an infinite sequence of elements belonging to {1,2,3,4,5,6}. A row is guaranteed to contain at least 2 of some element (since there are greater than 6 elements in the sequence). Let N be the width that separates these two identical elements in a row. Define the column to be an infinite sequence of rows. No two rows in a column can be identical, nor can any two adjacent sub-sequences (both) containing identical elements be identical, lest there exist a rectangle. An N-wide sub-sequence containing identical elements must exist and has only 6^N permutations. There are infinite unique rows in the column, but not infinite permutations of this sub-sequence. | ||
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evanthebouncy!
United States12796 Posts
On May 30 2009 00:17 King K. Rool wrote: Psuedo_Utopia has the same solution I worked out, so if it IS that solution, then I don't think this is really undergrad stuff, more like high-school math contest TBH (if you did good on contests, not trying to come off as pretentious). Seems like problem solving skills are enough to arrive at the proof, and requires no theorems or anything. right and you come to a thread titled "math puzzle" expecting things that requires stacked theorems. This problem is in chapter 1 of my Combinatorics book on pigeon hole principle. | ||
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