I was wondering whether I should ask for clarification about the seal on the envelope Krauss opened, since if it was an ordinary wax seal, it would’ve been highly improbable for anyone to have been able to pour molten wax on top of the letter to seal it while having dinner, and could’ve given me a reason to discard the “letter was prepared during the dinner” -approach. But I figured it would’ve been possible to bypass that issue by sealing the envelope in advance and cutting a hole in it through which the letter could be placed inside. Since the envelope wasn’t examined in detail, such a cut could’ve plausibly remained hidden until the culprit got their hands on the envelope and destroyed it, or somesuch.
Anyhow, now that you’ve directly confirmed that the letter couldn’t be written during the dinner, that point becomes moot. So, it’s time to refocus. Sadly, I have to get going for now, so the only thing I have to offer are my troll theories that I thought of a while ago.
The envelope actually contains a million letters that all contain a different number that Krauss guessed. Krauss just happened to pick the one that actually read his chosen number by coincidence. Also he somehow managed to not notice the 999999 extra letters in there. Maybe the paper was really thin.
Or… there was only one one letter, and it read that Krauss guessed 11037. However, there’s a red truth confirming that the letter would’ve included Krauss’ chosen number even if he had chosen differently. There is no contradiction… because the culprit wrote, in very tiny font in some extremely compact notation, all numbers Krauss could count in the letter with some extremely faint ink that is almost impossible to make out, and thus Krauss didn’t notice it. That way, all numbers Krauss could’ve guessed are “included” in the letter, even though only 11037 is visibly written in the paragraph talking about what number Krauss chose.