SOLUTION: How many positive integers have the same number of digits when written in base 5 and in base 8?

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: How many positive integers have the same number of digits when written in base 5 and in base 8?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1167770: How many positive integers have the same number of digits when written in base 5 and in base 8?
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


1-digit representations in base 5: 1-4
1-digit representations in base 8: 1-7
same number of digits in both bases: 1 to 4 (4 numbers)

2-digit representations in base 5: 5-24
2-digit representations in base 8: 8-63
same number of digits in both bases: 8 to 24 (17 numbers)

3-digit representations in base 5: 25-124
3-digit representations in base 8: 64-511
same number of digits in both bases: 64 to 124 (61 numbers)

4-digit representations in base 5: 125-624
4-digit representations in base 8: 512-4095
same number of digits in both bases: 512 to 624 (113 numbers)

There are no more; the smallest positive integer with a 5-digit representation in base 8 is 4096; the largest positive integer with a 5-digit representation in in base 8 is 3124.

ANSWER: 4+17+61+113 = 195