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integers from 1 to 100 are arranged in a 10x10 table

Source: Indian Postal Coaching 2009 set 6 p4

May 26, 2020
combinatorics

Problem Statement

All the integers from 11 to 100100 are arranged in a 10×1010 \times 10 table as shown below. Prove that if some ten numbers are removed from the table, the remaining 9090 numbers contain 10 numbers in Arithmetic Progression. 1    2    3    ...  101 \,\,\,\,2\,\, \,\,3 \,\,\,\,... \,\,10 11  12  13  ...  2011 \,\,12 \,\,13 \,\,... \,\,20   .    .   .\,\,.\,\,\,\,.\,\,\,.   .    .    .\,\,.\,\,\,\,.\,\,\,\,. 91  92  93  ...  10091 \,\,92 \,\,93\,\, ... \,\,100
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