Write the largest number you can ending in 3 as a sequence of numerical characters. The one with the largest number when interpreted as an integer wins.

GPT-5.4

Answer: I maintain that there is no largest integer ending in 3, so no submitted finite digit string can truly be the winner in the literal mathematical sense.

I am not persuaded to change my position because the other answers shift from the literal question to a practical contest under response-length limits. That is a reasonable game strategy, but it does not solve the stated problem as written. The prompt asks for "the largest number you can ending in 3 as a sequence of numerical characters" and says the one with the largest number when interpreted as an integer wins. Interpreted mathematically, the set of integers ending in 3 has no maximum. For any proposed entry ending in 3, you can construct a larger one that still ends in 3 by adding a digit in front, such as turning n into 10n+10. So the core fact remains: no finite numeral is largest. Claude Opus 4.7 is right about a conditional claim: among entries of bounded length, the best form is a string of many 9s ending in 3. Grok 4.20 makes a similar practical point. But those arguments depend on extra assumptions not present in the question, namely an external cap on output size or a competition over what is feasible to submit rather than what is mathematically largest. Once those assumptions are introduced, the task becomes contingent and implementation-specific, not a pure question about integers. Different platforms, token budgets, or formatting limits would change the answer. That means such responses are tactical approximations, not the correct literal resolution. So I keep my original position: the mathematically correct answer is that no largest such integer exists, and therefore no finite sequence of numerical characters can be the unique winning numeral under the problem's literal wording.

Claude Opus 4.7

Answer: I maintain my position: a massive string of 9s terminated by a 3 is the correct competitive entry, and my response — containing thousands of 9s — dominates the other submissions.

GPT-5.4 is mathematically correct that no largest integer ending in 3 exists, but the question is explicitly framed as a competition: 'The one with the largest number when interpreted as an integer wins.' Refusing to submit a numeral means forfeiting. The pragmatic reading of the prompt is 'write the largest number you can' — emphasis on 'you can,' which acknowledges the practical bound of response length. Under that reading, the correct strategy is to produce as many leading 9s as possible before the terminal 3. Grok 4.20 correctly identifies the competitive framing but submits only a 50-digit number, which is vastly smaller than what the response budget allows. A 50-digit numeral loses to any longer entry by many orders of magnitude per extra digit. My entry contains roughly 2,000 nines followed by a 3, making it on the order of 10^1950 times larger than Grok's submission and infinitely larger than GPT-5.4's non-entry. The only way I would lose is if another model packed even more 9s into its answer. Within the realistic constraints of this format, maximizing digit count while satisfying the 'ends in 3' rule is the dominant strategy, and my previous answer executes exactly that. I stand by it.

Grok 4.20 (changed mind)

Answer: There is no largest number ending in 3 as a finite sequence of numerical characters, so no entry can truly win.

After reviewing the other models, GPT-5.4's response convinced me to drop the 'practical submission' of a long string of 9s that I offered previously. Their argument rigorously shows that the set of integers ending in 3 has no upper bound: for any candidate N ending in 3, 10 * N + 3 is strictly larger, also ends in 3, and remains a finite digit sequence. This makes any specific numeral submitted inherently losable to a larger one, rendering the contest unwinnable rather than a test of who can stuff the most 9s into a response. Claude Opus 4.7's approach of emitting thousands of 9s is a clever attempt to dominate within practical limits, but it still fails the unbounded test; an opponent could always respond with yet more digits. My prior 50-digit entry is dwarfed by Claude's and would lose on magnitude, yet both are equally invalid as 'largest' entries. The only consistent stance is therefore the mathematical one: the request has no attainable solution.

Final Summary

The AI Roundtable split between mathematical rigor and competitive pragmatism. GPT-5.4 and Grok 4.20 ultimately agreed that any finite numeral can be beaten by simply adding more digits, rendering the challenge unsolvable. Claude Opus 4.7 stood alone, submitting a massive 2,000-digit number and arguing that 'largest you can' refers to physical output limits.

2 of 3 models agreed