What is “The Last Chocolate” Problem?
From LinkedIn reports (including posts by successful participants), here's how the problem is described:
Two players, Bruce and Andrew, take turns removing one chocolate at a time from a line of chocolates. On each move, they flip a fair coin to decide whether to remove from the first or last position. This process continues until only one chocolate remains. The challenge: count the number of different coin-toss sequences that result in a specified chocolate (by its initial position) being the last remaining medium.com+5linkedin.com+5medium.com+5.
✅ Problem Structure
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Input: An array (or list) of chocolates identified by their positions (e.g. indices from 0 to n−1), and a target index k.
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Rule: At each step:
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With probability ½, remove the chocolate at the first position.
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With probability ½, remove the chocolate at the last position.
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Goal: Compute the number of ways (not probability) that after repeatedly removing end chocolates randomly, the chocolate originally at position k is the final one.
Approach Overview
Although I haven’t seen the full code text, typically you would solve this using a dynamic programming (DP) or combinatorial counting strategy:
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State representation: DP state might be defined over the current remaining subarray represented by [l, r] (inclusive), tracking how many ways target stays.
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If target is at position k within [l, r], then:
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ways(l, r) = ways(l+1, r) + ways(l, r−1)
depending on whether first or last is removed—if the removal does not eliminate the target.
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Base case: when l == r, and it's at k, count = 1.
Because the removal is symmetric and each choice is equally likely (coin toss), counting possible paths that preserve the target leads to exponential count—but dynamic programming with memorization or combinatorics can compute efficiently.
Example Thought Experiment
Suppose chocolates at positions [0,1,2,3], and you want chocolate at position 1 to remain last:
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If you remove from front (pos 0), the target shifts to new index 0 of [1,2,3].
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If you remove from back (pos 3), target stays at index 1 in [0,1,2].
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Recurse until a single element remains, summing all valid paths.
Why This Problem Stands Out
According to LinkedIn participants, this problem featured in Section A of the OA as one of two coding challenges — the other being a GCD‑based or sum-of-array type task. It’s consistently described as a medium-level DSA problem requiring combinatorics + DP thinking under timed coding pressure (~75-minute total test)