Question

how many positive integers are there less than 800 such that all the digits are odd?

Answer 1

hey, how's it going?

Answer 2

good

Answer 3

so let's start with 1,3,5,7,9.

Answer 4

ok

Answer 5

that is a good base for us, because it's good to remember that there are 5 possibilities for the end digit

Answer 6

why

Answer 7

now what can the 2nd digit be? 1,3,5,7,9, of course

Answer 8

what i dont understand

Answer 9

so for up to 100, we have the 5 1-digit numbers, plus 5 possibilities for the tens digit, and there are 5 possibilities for the ones digit for each of those. so that's 25 more.

Answer 10

you understand so far? in the 10s, 11,13,15,17,19 work. that's 5. in the 30s, 31,33,35,37,39. 5. so there's a pattern. 5+5+5+5+5 = 25 numbers that have all odd digits from 10 to 99