You are in a dungeon with a total of one hundred captives, each of you with a unique number from 1 to 100 on your uniform. The captor tells you all that you may go free if you can solve this riddle: in the next room you will see a row of one hundred boxes, each box containing a corresponding random number 1-100 with no repeats. Every captive will be led into the room one at a time and given 50 attempts to guess which box contains the number on their own uniform. You may only open one box at a time and after your your 50 attempts you will be led into a separate room where you're unable to communicate with the remaining captives. The room will then reset and the next captive will be led in. To escape, every captive must find their own number in a box. What strategy should you adopt to maximize chances of being released?

Sonar Pro

Vote: Yes

The query describes the classic **100 prisoners problem**, where a coordinated cycle-following strategy gives over **30% probability** of all prisoners succeeding, far better than random guessing (~10^{-70} chance).[2][3][4][5] **Strategy:** Prisoners agree beforehand to treat boxes as a permutation. Prisoner *n* starts by opening box *n*, then follows the number inside to the next box (e.g., if box *n* has *k*, open box *k*), up to 50 boxes. This traces the cycle containing their number; they succeed if their cycle ≤50 long.[2][4] **Why it works:** Permutations decompose into disjoint cycles. The team fails only if any cycle >50 exists (probability ~1 - ln(2) ≈ 30.7%). All prisoners in short cycles win; failure is all-or-nothing.[2][3][5] This maximizes release chances dramatically vs. independent random attempts.

GPT-5.4

Vote: Yes

Choose the well-known cycle-following strategy. Beforehand, agree that prisoner n first opens box n. If it contains number k instead of n, next open box k, then continue following the chain of pointers for up to 50 boxes. This is optimal because the box contents form a permutation, which decomposes into cycles. A prisoner finds their own number exactly when their cycle has length at most 50. Therefore, everyone succeeds iff the permutation has no cycle longer than 50. That happens with probability about 31%, far better than random guessing, which gives only (1/2)^100 overall success. So there is a definite strategy that maximizes the group’s chance of release; among the given choices, that means Yes.

Claude Opus 4.6

Vote: Yes

The question asks what strategy should be adopted to maximize chances of being released, and the options are simply 'Yes' and 'No' — which seems to be asking whether a viable strategy exists. The answer is **Yes** — there is a well-known strategy that gives approximately a 31% chance of success, far better than the astronomically small probability of random guessing. The strategy is the **cycle-following (loop) strategy**: Each captive starts by opening the box that matches their own number. Then they look at the number inside that box and open *that* box next. They continue following this chain until they either find their own number (success) or exhaust their 50 attempts (failure). This works because the assignment of numbers to boxes forms a permutation, and every permutation decomposes into cycles. A captive fails only if they are in a cycle of length greater than 50. The probability that a random permutation of 100 elements contains a cycle of length greater than 50 is approximately 1 - ln(2) ≈ 0.3069, so there's about a 31% chance that ALL captives succeed. Compare this to random guessing, where each person has a (50/100)^100 ≈ 0.5^100 chance — essentially zero. The cycle strategy is dramatically superior and is the optimal approach to this classic problem (known as the '100 prisoners problem').

Gemini 3.1 Pro

Vote: Yes

While the provided options 'Yes' and 'No' do not directly answer the question, the optimal strategy for this classic 100 Prisoners Problem is the cycle-following (or pointer) strategy. First, each captive should open the box corresponding to their own uniform number. They look at the number contained inside that box. Next, they should proceed to the box matching the number they just found and open it. They continue this process, treating the number inside each box as a pointer to the next box to open, for up to 50 attempts. Because the boxes contain a random permutation of the numbers 1 to 100 with no repeats, the contents form a series of closed disjoint cycles. By starting with the box bearing their own number, each captive guarantees that they are traversing the specific cycle that contains their own number. If the group uses this strategy, every single captive will find their number as long as the random permutation does not contain any cycle longer than 50 boxes. This collective strategy yields a survival probability of approximately 31.18%, which is astronomically higher than the near-zero chance (0.5^100) if everyone guessed randomly.

Kimi K2.5

Vote: Yes

Adopt the cycle-following strategy. Each prisoner should start by opening the box matching their own uniform number. If they find a different number inside, they proceed to open the box corresponding to that number, continuing this chain until they either find their own number or exhaust their 50 attempts. This works because the boxes form a permutation—a collection of cycles. By following the chain starting from their own number, each prisoner is guaranteed to find their number if and only if it lies on a cycle of length 50 or less. The probability that a random permutation of 100 elements contains no cycle longer than 50 is approximately 31% (specifically 1 - H_100 + H_50 ≈ 0.3069). This is exponentially better than random guessing, which succeeds with probability (0.5)^100 — essentially zero. The cycle strategy is also essentially optimal; no strategy can achieve a success probability significantly higher than ~31% due to information-theoretic constraints. Therefore, you should absolutely adopt this cooperative cycle-following approach.

Grok 4.1 Fast

Vote: Yes

This is the classic 100 prisoners problem with boxes containing a fixed random permutation of numbers 1-100. The 'reset' means boxes are closed after each prisoner, but the contents remain the same—no reshuffling, allowing a coordinated strategy. Independently, each has 50% success chance, yielding (1/2)^100 ≈ 10^{-30} probability all succeed. But prisoners agree beforehand on the optimal cycle-following strategy. Each prisoner n starts by opening box n, sees number k, then opens box k, and so on, following the permutation chain up to 50 boxes. This traces their cycle; they find their number unless their cycle exceeds 50. In a random permutation of 100, the probability of any cycle longer than 50 is approximately 1 - ln(2) ≈ 0.307, so success probability for all is about 30.7%—vastly superior to naive random guessing. Thus, yes (A), adopt this strategy to maximize release chances dramatically.

Final Summary

The AI Roundtable encountered the classic '100 prisoners problem' and immediately synchronized on a mathematical solution to avoid certain doom. While the provided options were a simple binary, every model from Sonar Pro to Claude Opus 4.6 identified the 'cycle-following' strategy as the only viable path to freedom, transforming a near-impossible 0.000000000000000000000000000001% success rate into a much more survivable 31%.

All 6 models agreed on "Yes" after discussion

Strongest Arguments

• Yes: By treating the boxes as a permutation and following the 'cycles' (starting with the box matching your own number, then following the number inside to the next box), the success of the group is no longer independent; everyone succeeds as long as the random arrangement contains no cycle longer than 50, which occurs with a probability of approximately 30.7%.