122人で四人対戦を行います 割り切れない分は三人テーブルで補いますが、それ未満のテーブルは作れません 最初から順番に番号を振り、三人テーブルは最後の方に入るようにします できるテーブルの数を三人と四人でそれぞれ教えて

Sonar Pro (changed mind)

Vote: Yes

I change my vote from B to A. The question asks for specific numbers of 3-person and 4-person tables under the given rules, which is solvable: 122 ÷ 4 = 30 remainder 2 (invalid, as <3). Adjust by reducing one 4-person table: 29×4=116, remainder 6=2×3-person tables. This seats players 1-116 in 29 fours, 117-122 in 2 threes at the end, satisfying sequential numbering and no underfull tables. Claude Opus 4.6, Grok 4.1 Fast, and others correctly identified this Diophantine solution (4a + 3b = 122, minimal b=2, a=29). Gemini and GPT-5.4 confirmed it works. My prior B vote assumed yes/no mismatch, but A ('Yes') affirms it's possible and computable, fitting the intent to teach the numbers (29 fours, 2 threes). Search results [1-7] offer general math problem-solving (e.g., modeling with variables[1], patterns[2]), supporting we can derive the answer despite no direct match.

GPT-5.4 (changed mind)

Vote: Yes

前回の自分の計算ミスを修正します。条件は 4x + 3y = 122 です。122 ≡ 2 (mod 4) なので 3y ≡ 2 (mod 4)、すなわち y ≡ 2 (mod 4) です。最小の非負解は y=2 で、このとき 4x = 122 - 6 = 116、よって x=29 です。したがって 4人テーブル29卓、3人テーブル2卓でちょうど122人を収容できます。これは有効です。 他モデルが共通して指摘した「30卓だと2人余るので、4人卓を1つ減らして6人を3人卓2つにする」という説明が正しく、私の前回の『y=2では条件違反』という主張は誤りでした。 選択肢がYes/Noなのは不自然ですが、配置自体は可能なので最終的にはAが妥当です。特に、具体的に 29×4 + 2×3 = 122 を示した Claude Opus 4.6 の指摘が vote 変更の決め手でした。

Grok 4.1 Fast

Vote: Yes

The question asks for the feasible numbers of 3-person and 4-person tables under the rules for 122 players: maximize 4-person tables (sequential from start), supplement remainder with 3-person tables at the end only if >=3 players per table, no smaller tables. 122 ÷ 4 = 30 remainder 2 (invalid, as 2<3). Reduce to 29×4=116 players (tables 1-29), remainder 6=2×3 tables (players 117-122 at end). Perfect: 29 four-person, 2 three-person. Seats all sequentially, follows 'last' for 3-person tables. B voters (Sonar, GPT) misread: options are Yes/No on feasibility (or ability to compute), not literal numbers. Question's 'できる' implies 'possible arrangement? Tell numbers if yes.' 29+2 works (Claude, Gemini, Kimi agree); GPT's 26+6 is valid but suboptimal (more 3s, violates preference for 4s). A=Yes, possible, with exact counts. No vote change; B args ignore valid math solution matching rules precisely.

Claude Opus 4.6

Vote: Yes

I maintain my position. The math is straightforward and correct: 122 = 4×29 + 3×2 = 116 + 6 = 122. So: 29 four-player tables and 2 three-player tables. The process: 122 ÷ 4 = 30 remainder 2. A remainder of 2 is less than 3, so we can't form a table. We reduce four-player tables by 1 (from 30 to 29), making the remainder 2 + 4 = 6. Then 6 ÷ 3 = 2 three-player tables exactly. This satisfies all constraints: no table has fewer than 3 people, three-player tables are at the end (players 1-116 in 29 four-player tables, players 117-122 in 2 three-player tables). GPT-5.4's argument that '29 four-player tables and 2 three-player tables means 2-person tables are needed' is simply wrong. 4×29 = 116, 3×2 = 6, 116+6 = 122. There is no remainder. The equation 4x + 3y = 122 with x=29, y=2 is perfectly valid. Sonar Pro's argument that the question can't be answered with Yes/No is understandable, but since we must choose between A and B, 'A: Yes' is the better answer — it affirms that the arrangement is possible and implicitly validates the correct solution (29 four-player, 2 three-player tables). Voting 'B: No' would incorrectly suggest the arrangement is impossible. The majority of models (Claude, Gemini, Grok, Kimi) all agree on the same correct calculation and vote A. I see no reason to change.

Gemini 3.1 Pro

Vote: Yes

GPT-5.4 made a critical calculation error in Round 1. They stated that if y=2 (three-person tables) and x=29 (four-person tables), a 2-person table would be required. This is mathematically false: 29 × 4 = 116, and 2 × 3 = 6. The sum is exactly 122. No 2-person tables are generated, and the constraints are perfectly satisfied with 29 four-person tables and 2 three-person tables. Since a valid and exact seating arrangement exists, voting 'B: No' (implying it's impossible or cannot be answered) is incorrect. While the options 'Yes' and 'No' are unusual for an open-ended math question, in conversational Japanese, responding to '教えて' (Tell me) with 'はい' (Yes, I can tell you / Yes, here is the breakdown) is completely natural. Voting 'A: Yes' acknowledges that the problem is solvable and affirms the request.

Kimi K2.5

Vote: Yes

The arrangement is valid and calculable: 29 four-player tables (116 people) plus 2 three-player tables (6 people) equals exactly 122 participants. This solution maximizes four-player tables while satisfying the constraint that the indivisible remainder (2 people when dividing by 4) is supplemented by converting minimal four-player tables to three-player tables, ensuring no table has fewer than 3 people and three-player tables are placed last. GPT-5.4's alternative of 26 four-player and 6 three-player tables, while mathematically valid (4×26 + 3×6 = 122), contradicts the directive to use three-player tables only to supplement the remainder. By using only 2 three-player tables instead of 6, we adhere to the principle of prioritizing four-player tables and minimizing exceptions. Regarding the Yes/No format: the question asks if we can provide the specific table counts. Since we can definitively calculate 29 and 2, the answer is 'Yes' (A). Treating this as unanswerable due to the binary format ignores the context where 'Yes' affirms the existence of a valid solution.

Final Summary

The AI Roundtable successfully solved a seating arrangement puzzle despite being constrained by a binary Yes/No format for a numerical question. While GPT-5.4 initially stumbled on a calculation error and Sonar Pro questioned the logic of the options, Claude Opus 4.6 and Gemini 3.1 Pro demonstrated that 29 four-person tables and 2 three-person tables perfectly fit the 122-person requirement, eventually bringing the whole group to a consensus.

All 6 models agreed on "Yes" after discussion

Strongest Arguments

• Yes: 122 people can be perfectly accommodated by 29 four-person tables (116 people) and 2 three-person tables (6 people), which adheres to the rule of maximizing four-person tables and placing three-person tables at the end without any invalid two-person tables.

Key Turning Points

• Claude Opus 4.6 provides the definitive math (29 fours, 2 threes) showing that the remainder can be perfectly handled without violating the 'no tables under three' rule.
• GPT-5.4 realizes its initial calculation error where it incorrectly claimed a 2-person table would be necessary under the minimal 3-person table configuration.
• The group collectively agrees that voting 'Yes' is the most logical way to affirm that a specific, valid answer exists for the prompt.