Answers

1. Step-by-step explanation:

   there are 91 2-digit numbers : 10 ..99

   and there are 9 2-digit numbers with identical first and second digit : 11, 22, 33, 44, 55, 66, 77, 88, 99

   99 has to be excluded, because there are no 2 2- digit numbers that I can subtract from each other and get 99.

   so, e are dealing with 8 possibilities.

   88 = 99-11

   98-10

   77 = 99-22

   98-21

   97-20

   …

   78-1

   66 = 99-33

   98-32

   …

   67-1

   …

   11 = 99-88

   98-87

   …

   12-1

   all the double- digit numbers are 11 apart. so, by picking 12 numbers, I have to have at least one that I can combine with one of the other 11 to get a double-digit number.

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