Question

Write the smallest 8digit numbr having five different digit

Answer 1

Answer:

Let’s go with positive integers only, in base ten, just to simplify things.

We’ll have to lead with a non zero digit, because leading zeros get dropped, so we wouldn’t have an eight digit number. For example, 03 is not a two digit number, it’s just the single digit number 3.

Since the first digit is the highest value, we’re going to want to use the lowest non zero digit in that spot, so our number will be 1nnnnnnn

Zero is the lowest digit, we’re going to want to use those as much as possible. 10000000 is the lowest eight digit number for those reasons. But it only has two different digits. So that’s not it.

To get to five digits, we’ll start with the lowest and work our way up, least possible digits to use. 0 and 1 we were already using, but to get to five we need three more, 2, 3 and 4.

That in turn means we get to use one of the digits three extra times. Zero is the lowest digit, so we’ll use that one. And we’ll put them in the highest spots: consider, 120 is more than 102. Lowest numbers for the highest slots, sort out the lower slots when you get to them. So our number will be 10000nnn, using zeros in all the highest slots we can.

For similar reasons, we’ll put the 2 rather than the 3 or 4 in the thousands slot, and again for the same reason, pick the 3 next, leaving the 4, our largest digit, in the units slot where it does the least damage.

Final answer is 10000234.