I think we are introducing too much context to the question that sums up to "is it capable of reasoning?"
To answer this question one needs to remove unnecessary context.
GPT-4 can’t sum two unusually big integers.
This is as context-free as it gets. Ability to pass this test wouldn’t be conclusive, but the inability seems to be conclusive that it isn't capable of reasoning.
With this fact in mind explaining why it can't solve a logical riddle is pointless.
To answer this question one needs to remove unnecessary context.
GPT-4 can’t sum two unusually big integers.
This is as context-free as it gets. Ability to pass this test wouldn’t be conclusive, but the inability seems to be conclusive that it isn't capable of reasoning.
With this fact in mind explaining why it can't solve a logical riddle is pointless.