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Algebra Difficulty 1.9 Junior Find the answer

How many of the integers from 1 to 100, inclusive, have at least one digit equal to 6?

A number or a short expression. Spacing and $ signs are ignored.

Solution

The integers between 1 and 100 that have a ones digit equal to 6 are 6,16,26,36,46,56,66,76,86,966, 16, 26, 36, 46, 56, 66, 76, 86, 96, of which there are 10. The additional integers between 1 and 100 that have a tens digit equal to 6 are 60,61,62,63,64,65,67,68,6960, 61, 62, 63, 64, 65, 67, 68, 69, of which there are 9. Since the digit 6 must occur as either the ones digit or the tens digit, there are 10+9=1910 + 9 = 19 integers between 1 and 100 with at least 1 digit equal to 6.

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Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.