Prove it – Ep5: Perpetual Children
Let’s follow an algorithm:
- Determine heuristic used in example.
- Summarize math solution.
- Define new heuristic, if possible.
- Discuss Claude’s math solution.
- Provide dashboard solution, if possible.
Heuristic:
Analysis of this problem indicates a heuristic is challenging. You either reach parity, or seem to get further away.
Mathematical solution:
Use random walk as solution basis. Reduce problem to counting paths in sub-square. Reduces to Catalan numbers – 1/(n+1)(2n n)
Simplifies to lower bound – # of terms in the sum * largest term in the sum.
E(X) > 1/2 Sigma 1/n; n: 1 to inf.
New heuristic
Same.
Claude math
Very interestingly defines situation as “gambler’s ruin”
The desire is to “get back to even” when this may take until infinity. Although, perhaps comfortingly, it will happen there! This is because it’s a convergent problem.
Efehn’s puzzles completely changed how I think—so engaging and rewarding!
Sarah Lee
Puzzle Enthusiast – Not a real person