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February 8, 2016
Posted by **jason** on Sunday, March 6, 2011 at 2:34pm.

- math -
**MathMate**, Sunday, March 6, 2011 at 3:08pmThe digits of a base 10 number goes from 0 to 9. The first digit of a two digit number (any base) cannot be zero, otherwise the number will become a 1-digit number.

So in base 10, there are 9 choices for the first digit, and 10 choices for the second, for a total of 9*10 numbers.

For a number in base 5, we have up to 5 different digits, namely 0,1,2,3,4. The digit 5, 6, ... do not exist in a number to base 5.

So the number of choices for the first digit, excluding zero, is 5-1=4. The number of choices for the second digit is 5.

So there is a total of 4*5 =20 two digit base 5 numbers, namely

10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31.....34, 40, 41, 42, 43, 44.

(Remember digits 5 and above do not exist in base 5, just like we have no digit for 10 and above for base 10).

If this is still not clear, please post.

- math -
**jason**, Sunday, March 6, 2011 at 3:29pmMathmate-

Thank you very much, I completely understand your explanation now.

- math :) -
**MathMate**, Sunday, March 6, 2011 at 3:44pm:)