There is phone keyboard with Knight on 0 (as shown below).
123
456
789
0
Knight moves as per the rules of chess (2 straight and one turn).
T is no. of moves by knight and S is sum of key's values where knight moves.
After T = 1024 moves, What will be the probability that S is divisible by 5 given that it is already divisible by 7.
I tried by drawing a tree structure and found that sum S would occur in odd-even pattern in alternate values. I also found the range of values of S after T = 1024 moves. But I couldn't proceed further.