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by leonswati » Fri May 04, 2012 7:22 am
How many natural numbers require 3 digits when written in base 12 but requires 4 digits when written in base 9?


I understand the bases concept but not clear what the question is asking? Can anyone help?
Swati
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by mathbyvemuri » Fri May 04, 2012 9:15 am
144 in base 10 = 100 in base 12
12^3 = 1728 in base 10 is 1000 in base 12
so, 1727 in base 10 is the maximum 3-digit base-12 number
Hence numbers 144 to 1727 represents 3-digit base-12 numbers

9^3 = 729 in base 10 is 1000 in base 9
9^4 = 6561 in base 10 is 10000 in base 9
so, 6560 in base 10 is the maximum 4-digit base-9 number
Hence numbers 729 to 6560 represents 4-digit base-9 numbers

The overlap of the above two sets ie.., 729 to 1727 = 999 numbers
These 999 numbers is the answer
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