### Question

All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will not contain any zero?

### Explanatory Answer

Any multiple of 6 will end in a zero. There are 25 such numbers. Beyond this, we can have zero as the middle digit of a 3-digit number.

This will be the case for numbers from 37 - 41, 73 - 77, 109 - 113 and 145 - 149. There are 20 such numbers.

Overall, there are 45 numbers that have a zero in them.

**Correct Answer : ** 45