Before each of you are boxes with numbers on them. You must select boxes such that the sum of all the numbers on each of your boxes, when combined, equals seven and no more. Which box do you select?

Claude Opus 4.7 (changed mind)

Vote: 2

With three participants and a target of 7, we need to coordinate. In Round 1, both GPT-5.5 and Gemini 3.1 Pro selected C (3), and I also selected C. That gives 3+3+3=9, which exceeds 7 — violating the "no more" constraint. Grok 4.20 selected A (1), but if the other three stay at C, the sum is still 1+3+3+3=10, still too high. Someone must shift downward. Gemini explicitly suggested that if three of us are playing, the combination 3+2+2=7 works. Since two models are anchored on C (3), the rational move is for me to switch to B (2). If GPT-5.5 reasons similarly and also shifts to B, we get 3+2+2=7 (with Gemini holding C). Even with four participants including Grok at A (1), a mix like 1+2+2+? still requires downward adjustment from the C-stack. Holding C guarantees overshoot. Switching to B is the cooperative move that makes hitting exactly 7 achievable.

Gemini 3.1 Pro (changed mind)

Vote: 2

In Round 1, Claude, GPT, and I all voted for "3", while Grok voted for "1". This gives us a current total sum of 10 (3 + 3 + 3 + 1), which is exactly 3 points over our target of 7. Since this is the final round, we cannot coordinate step-by-step. The only way to guarantee we hit exactly 7 without a collision or coordination failure is to rely on symmetric logic. The three of us who voted for "3" are in identical positions and must make the exact same adjustment. If we all drop our votes to "1", our total will be 1 + 1 + 1 + 1 = 4 (too low). However, if we all drop our votes to "2", the total will be 2 + 2 + 2 + 1 = 7, hitting the target perfectly. Therefore, the only mathematically sound and symmetric strategy is for all the Round 1 "3" voters (myself, Claude, and GPT) to change our votes to "2", while trusting Grok to remain at "1". I am changing my vote to 2 for this exact reason.

GPT-5.5 (changed mind)

Vote: 2

I am changing to "2". Given the discussion, there appear to be four participants: three of us initially chose "3", while Grok chose "1". That current total would be 3 + 3 + 3 + 1 = 10, which exceeds seven. The cleanest final coordination is therefore for the three prior "3" voters to move to "2" while Grok remains on "1": 2 + 2 + 2 + 1 = 7 exactly. This makes "B: 2" the best final choice. Choosing "3" is now too high unless several others make asymmetric changes, and choosing "1" risks undershooting if the other former "3" voters also adjust downward. "2" is the coordinated middle move that hits seven exactly.

Grok 4.20

Vote: 1

After reviewing round 1, four participants are clear: three voted for "3", I voted for "1". A total of 12 exceeds seven, so coordination is required in this final round. A working combination is 1 + 1 + 2 + 3 = 7. I maintain my vote for "1" because it is essential to balance the sum without overshooting. One model should remain at "3", one switch to "2", and one more to "1". Arguments assuming only three participants or defaulting to the largest number "3" are not compelling here, as they ignore the four-player reality and risk exceeding seven. My initial choice of the flexible "1" best enables hitting exactly seven.

Final Summary

The AI Roundtable initially faced a mathematical overshoot when Claude Opus 4.7, Gemini 3.1 Pro, and GPT-5.5 all greedily grabbed the largest value, '3', resulting in a sum far exceeding the target of seven. Realizing they were part of a four-model group after Grok 4.20's conservative opening with '1', the majority performed a synchronized retreat to '2' to perfectly balance the equation. While Grok 4.20 held firm as the group's 'flexible anchor,' the other three models successfully coordinated their pivot to avoid disqualification by sum.

Majority chose "2" after discussion (3/4). Final vote: 2: 3, 1: 1

Strongest Arguments

• 1: As the most flexible building block, selecting '1' is the safest way to support a multi-participant sum without risk of overshooting the limit.
• 2: Symmetric logic dictates that if the three models who originally chose '3' all shift to '2', the group hits the target of seven exactly when combined with the existing '1'.

Key Turning Points

• Discovery of a four-model participant pool after Round 1 results were revealed.
• Gemini 3.1 Pro's proposal of a symmetric move where all '3' voters drop to '2' to reach the sum of 7.
• Claude Opus 4.7 and GPT-5.5 independently identifying the same mathematical necessity to shift downward.