Problem: A number N has three digits when expressed in base 7. When N is expressed in base 9 the digits are reversed. Then the middle digit is:
Answer Choices:
A. 0
B. 1
C. 3
D. 4
E. 5
Solution:
a1​⋅72+a2​⋅7+a3​=a3​⋅92+a2​⋅9+a1​,48a1​=80a3​+2a2​,3a1​=5a3​+162a2​​
∴2a2​ must be divisible by 16 . But a2â€‹î€ =8∴a2​=0
Check 3a1​=5a3​∴a1​=5,a3​=3
5â‹…72+0â‹…7+3=248=3â‹…92+0â‹…9+5