Everyone seems to have forgotten the rooms 90, 91, 92, etc.
Here's a breakdown for each digit, how many times it will be painted and what rooms have those digits:
0: 11 times = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
1: 21 times = 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, 100
2: 20 times = 2, 12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 42, 52, 62, 72, 82, 92
3: 20 times = 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93
4: 20 times = 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, 94
5: 20 times = 5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 56, 57, 48, 59, 65, 75, 85, 95
6: 20 times = 6, 16, 26, 36, 46, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 86, 96
7: 20 times = 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97
8: 20 times = 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98
9: 20 times = 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
There are 19 rooms that have '9's on them, but room 99 has it twice. As you can see, the number 9 will be painted *20* times.
An easy way to think of it, is it will appear 10 times as a tens digit, and 10 times as a unit digit. That's a total of 20 times.
2006-06-20 11:20:19
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answer #2
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answered by Puzzling 7
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