How many of the 343 smallest positive integers written in base 7 use 4 or 5 (or both) as a digit?
Ill add the word positive. Smallest positive integers.
343 base10
7^3=343
so 343 base10 = 1000 base 7
There are a total of 343 numbers.
Lets think about the base 7 number. And first I am only going take a look at the ones less than 1000 base 7
The 7^2 digit can be 0 to 6 that is 7 digits
The 7^1 digit can be 0 to 6
The units digit can be 0 to 6 so long as the number is less than 1000 base7
How many have numbers less than 1000 base 7 have NO 4 or 5.
Each digit can be 0,1,2,3 or 6
5*5*5 = 125
[I have actually included 000 and not included 1000 but one in one out makes no difference]
So that is 125 that do not have a 4 or a 5
343- 125 = 218
So I think 218 do have a either a 4 or a 5 or both.