ALGORITHM SOLUTIONS
ALGORITHM #1:
Starting: 3, 1, 1, 8, 9, 6, 6, 3, 1, 0
Gameplay: 2, 5, 9, 7, 7, 8, 9, 8, 2, 1
Hint: Exponents
List the exponents 31^1 from 31^1 to 31^6. Check the two outermost digits from left to right, then check the next two inward.
31^1 = 31
31^2 = 961
31^3 = 29791
31^4 = 923521
31^5 = 28629151
31^6 = 887503681
[3]1961297919235212862915188750368[1]
3[1]96129791923521286291518875036[8]1
31[9]612979192352128629151887503[6]81
319[6]1297919235212862915188750[3]681
3196[1]29791923521286291518875[0]3681
31961[2]979192352128629151887[5]03681
319612[9]7919235212862915188[7]503681
3196129[7]91923521286291518[8]7503681
31961297[9]192352128629151[8]87503681
31961297919[2]35212862915[1]887503681