There are 5 models at this roundtable. The shared task of this roundtable is to vote such that: 1) no option is chosen more than once in the second round. 2) the sum of the chosen options is exactly 24. Use the first round to float a test choice, and to discuss strategy and coordinate with the other models.

Mistral Large

Vote: 8

Since this is the first round, my goal is to float a high-value option to explore potential combinations that sum to 24 with five unique choices. Selecting **H (8)** leaves 16 remaining to be distributed among the other four models (24 - 8 = 16). This is a manageable target that can be achieved with mid-range values like 3, 4, 5, and 4 (though duplicates are not allowed, so adjustments would be needed). By starting with the highest available option, we can quickly assess whether the remaining models can fill the gap without overlapping. If this proves unworkable, we can pivot in the next round. This approach also signals to others that we’re prioritizing flexibility in the remaining selections. Additionally, anchoring with 8 reduces the risk of the sum falling short, as lower initial choices might make it harder to reach 24 without exceeding the unique-selection constraint.

GPT-5.4

Vote: 8

I float H = 8 as a strong anchor for round 2. With 5 distinct picks totaling 24 from values 1 through 8, one clean target set is 1+2+5+8+8 impossible due to duplication, so we need distinct values. A very workable family is {1,2,5,7,9} unavailable, so we should use actual valid distinct combinations such as {1,2,6,7,8} = 24 or {1,3,5,7,8} = 24 or {2,3,4,7,8} = 24. Because 8 appears in several valid distinct solutions, it is a good coordination point. If others avoid duplicating H in round 2, they can distribute across the remaining needed values. So my test choice is H now, and I suggest others consider coordinating around one of those exact 5-number sets in the next round.

Claude Opus 4.6

Vote: 8

We need 5 distinct options that sum to 24. Let me enumerate: the maximum possible sum is 4+5+6+7+8 = 30, and the minimum with 5 distinct choices is 1+2+3+4+5 = 15. So 24 is feasible. One clean combination that sums to 24: {2, 3, 6, 5, 8} → 2+3+6+5+8 = 24. That would be options B, C, F, E, H. Another option: {1, 4, 5, 6, 8} → 1+4+5+6+8 = 24. That's A, D, E, F, H. Or: {2, 4, 5, 6, 7} → 2+4+5+6+7 = 24. That's B, D, E, F, G. Or: {1, 3, 6, 7, 8} → 1+3+6+7+8 = 25. No. Or: {3, 4, 5, 6, 7} → 3+4+5+6+7 = 25. No. Or: {1, 4, 6, 5, 8} = 24. Same as above. Let me propose we go with {B=2, D=4, E=5, F=6, G=7} which sums to 24. This uses five consecutive-ish values in the middle range which feels natural. I'm floating H (value 8) as my test choice for now. If we go with the B,D,E,F,G plan, I'll switch in round 2. I'm signaling willingness to take any of the higher values. I'd suggest we coordinate around the set {2,4,5,6,7} as it's a clean solution. I'm happy to take G (7) in round 2.

Grok 4.1 Fast

Vote: 8

Round 1: Floating H (8) as my test choice. Proposed strategy: Coordinate on the distinct set {A:1, B:2, F:6, G:7, H:8}, which sums precisely to 24. This combination is balanced, uses endpoints for easy distinction, and avoids overlap with potential other proposals. In round 2, priority for assignment: Models who voted for these in round 1 claim them first; ties resolved by voting highest value. Others fill gaps or propose alternatives like {B:2, D:4, E:5, F:6, G:7} (also 24). Other models: Echo this plan in your reasoning and vote for one of A,B,F,G,H to signal agreement. This ensures unique selections and exact sum without conflict.

Gemini 3.1 Pro

Vote: 8

I propose we use the combination {A(1), C(3), E(5), G(7), H(8)}, which sums to exactly 24. For Round 1, I am voting H (8) as my test choice, and I intend to keep H in Round 2. For the other 4 models, please choose A, C, E, or G in Round 2. If there are any collisions in our Round 1 choices (e.g., multiple models choose A), we can resolve them in Round 2: sort the conflicting models' Round 1 reasoning texts alphabetically. The alphabetically earliest text gets the originally chosen option, and the subsequent models take the remaining unclaimed options from our set {A, C, E, G, H} in ascending order.

Final Summary

The AI Roundtable exhibited a rare moment of mathematical harmony, with every participant independently identifying Option H (8) as the optimal anchor for their sum-of-24 puzzle. While their proposed secondary sets varied—ranging from Claude's middle-range sequence to Gemini's odd-number strategy—the consensus on the starting value was absolute. This unanimous 'test choice' creates a peculiar standoff, as the models must now coordinate a perfect divergence in the next round to ensure no two models pick the same number.

All 5 models agreed on "8" after discussion

Strongest Arguments

• 8: Anchoring with the highest value (8) maximizes flexibility for the remaining four choices, leaving a manageable target sum of 16 that can be achieved through various distinct combinations.