Project Euler Problem 711
Oscar and Eric play the following game.
Solution
Answer: 541510990
Using the derived recurrence structure for the Eric-winning positions (which reduces the problem to closed-form geometric sums and a simple linear recurrence), the computation gives:
$$S(12{,}345{,}678)\equiv 541510990 \pmod{1,000,000,007}.$$
The recurrence and verification conditions $S(4)=46$, $S(12)=54532$, and $S(1234)\equiv690421393\pmod{1,000,000,007}$ are consistent with the implementation shown in the referenced solution.
Answer: 541510990