Sweet chocolate

What this chocolate-bar probability question tests

This is a medium-difficulty probability problem that rewards careful case analysis and systematic thinking about sequential random processes. It asks you to reason about the final state of a procedure where each step removes either a row or a column from a grid, and to calculate the probability of a specific terminal condition.

To solve problems like this, candidates typically enumerate the possible sequences of moves that lead to the target outcome, account for the symmetry or structure of the problem, and use conditional probability or combinatorial counting. The key insight is recognizing which sequences of choices result in the top-left square being the sole remaining piece, then weighing those sequences by their individual probabilities.

• Sequential decision processes and state transitions
• Combinatorial counting of paths
• Probability of compound events under uniform random choice