What single digit appears most frequently between and including the numbers 1 and 1,000 Hint: look for a pattern?

Answer 1

The single-digit that appears most frequently between and including the numbers 1 and 1000 is the digit "1". To see why this is the case, consider the following pattern:

• Between 1 and 9, there is one occurrence of the digit "1".

• Between 10 and 99, there are 10 occurrences of the digit "1" in the tens place (10, 11, 12, ..., 19) and 9 occurrences of the digit "1" in the ones place (21, 31, 41, ..., 91), for a total of 19 occurrences.

• Between 100 and 999, there are 100 occurrences of the digit "1" in the hundreds place (100, 101, 102, ..., 199), 100 occurrences of the digit "1" in the tens place (110, 111, 112, ..., 119, 121, 131, ..., 191, 201, ..., 291, 301, ..., 391, ..., 901, ..., 991) and 9 occurrences of the digit "1" in the ones place (101, 111, 121, ..., 191), for a total of 210 occurrences.

Adding up the number of occurrences for each range, we get:

1 + 19 + 210 = 230

Therefore, the digit "1"