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Combinatorics (from Irish MO)

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December 17, 2015
combinatoricscombinatorics unsolved

Problem Statement

(a) In how many ways can 10031003 distinct integers be chosen from the set {1,2,...,2003}\{1, 2, ... , 2003\} so that no two of the chosen integers di ffer by 10?10? (b) Show that there are (3(5151)+7(1700))1017(3(5151) + 7(1700)) 101^7 ways to choose 10021002 distinct integers from the set {1,2,...,2003}\{1, 2, ... , 2003\} so that no two of the chosen integers diff er by 10.10.
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