Easy number theory.
 

:question:
A 3 digit number in the scale of 7 has its digits reversed when expressed in the scale of 9. Find the number in all three scales, 7 ,9 and 10.
Mally :coffee:

[spoiler]49k+7m+n = 81n+9m+k

48k-2m-80n = 0
24k-m-40n = 0

1<=k<=6
0<=m<=6
1<=n<=6

m must be multiple of gcd(24,40) = 8, so m=0

m = 0 -> 24k-40m = 0 -> k=5, n=3

So the number in base 7 is 503 (248 decimal), which is equal to 305 in base 9.[/spoiler]

Easy number theory.
 

:redface:
Fine deduction Alpertron!
I thought the digit 8 coming in to the calculations would stump any one in forming the equations.
I must bear you in mind when I give my next problem and make it more challenging.
Mally :coffee: