Prove it – Ep4: A Dicey Interview Question
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.
Claude prompt:
You are rolling a set of N dice at the same time. Your goal is to get exactly one 6. What is the optimal choice for N?
Heuristic:
5 or 6 dice seems like a good guess to get exactly one 6 since a 6 is obviously 1/6 chance.
Mathematical solution:
Calculate the probability of exactly one 6. (n/6)(5/6)^(n-1) then maximize expression. Assume continuous and then differentiate.
n= -1/ln(5/6) ~ 5.5
Choose either 5 or 6. No preference.
New heuristic
Can’t really think of one. Same as original.
Claude math
Chooses 5 since its has a 40.2% chance vs. 40.1% for 6.
Very interesting in that it illustrates the sometimes binary nature of an LLM (large language model)
Efehn’s puzzles completely changed how I think—so engaging and rewarding!
Sarah Lee
Puzzle Enthusiast – Not a real person