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Bornach

Gemini reveals more of its "thinking" than ChatGPT so I can check where it seems to have gone wrong. The wildly incorrect answer seems to have come out of nowhere but mentioning an "online calculator"

One has to guess where o3mini might have made its mistake in the summarised chain of thought.

For 3x5 board with one corner missing, answer is 1249. We are asked for the number of ways. We found that it is possible to tile. And online calculator gives 1249. Since we are asked for a specific number, it is likely that there is a method to calculate it. Maybe we need to use Pfaffian orientation and determinant, but it is complex.
Excerpt of ChatGPT chain of thought summary Tiling Column 1. When “advancing” from the (virtual) “column 0” (which is “empty”) to column 1 one must “tile” the available four cells in column 1. (Recall that a domino that “leaves” column 1 will cover one square in column 1 and one in column 2.) One may show that there are exactly five “local” tiling‐patterns for column 1. For example, one may either tile all available squares by vertical dominoes (covering (2,1)–(3,1) and (4,1)–(5,1)) or “mix” vertical dominoes with horizontal ones (for instance, using a vertical domino on (2,1)–(3,1) and covering (4,1) and (5,1)
Feb 08, 2025, 03:06 PM·Quiet public·Web
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