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:
a1ββ
72+a2ββ
7+a3β=a3ββ
92+a2ββ
9+a1β,48a1β=80a3β+2a2β,3a1β=5a3β+162a2ββ
β΄2a2β must be divisible by 16 . But a2βξ =8β΄a2β=0
Check 3a1β=5a3ββ΄a1β=5,a3β=3
5β
72+0β
7+3=248=3β
92+0β
9+5