How many digits have ''6''between 1 and 999?

Answer 1

The only number with a 6 between 1 and 9 is 6.

Between 10 and 99, every number that ends in a 6 or is in the sixties will have a 6 in it. The former category has 9 numbers in it, the latter 10, but they overlap at 66 so there are 18 numbers total in the range.

Fromm 100 to 999, the number must have a 6 in either the ones, tens, or hundreds digit. 90 numbers have a 6 in the ones place, 90 again in the tens place, and 100 in the hundreds place. NOT including the number 666, there are 8 overlaps that have 6 in both the ones and tens place, 9 with 6 in the ones and hundreds place, and 9 with 6 in the tens and hundreds place. Finally, the number 666 was counted an extra two time. Subtracting all the double/triple appearances, there are 252 numbers with a 6 in this range.

Finally, add up all these ranges to get that there are 271 numbers numbers with the digit 6 in this range.