Problem 165

The integers between 1 and 100 that have a ones digit equal to 6
are $$6, 16, 26, 36, 46, 56, 66, 76, 86, 96$$ of which there are 10.

The additional integers between 1 and 100 that have a tens digits equal
to 6 are $$60, 61, 62, 63, 64, 65, 67, 68, 69$$ of which there are 9. (Note that 66 was included in the
first list and not in the second list since we are counting integers
rather than total number of 6s).

Since the digit 6 must occur as either the ones digit or the tens digit,
there are $10 + 9 = 19$ integers
between 1 and 100 with at least 1 digit equal to 6.