[pdurrant]

Originally Posted by obs20

Spoiler:

The first night they are captive so on the second night

If wise guy A sees 13 then wise guy B sees 0
they go home that second night

Same if wise guy A sees 12 then wise guy B sees 1
they go home that night because wise guy A knows there cannot be 10

Same if Wise guy A sees 11 and wise guy b sees 2
If wise guy A sees 10 then wise guy B sees 3 or 0
because wise guy B knows that if Wise guy A
saw 13 they'd gone home the second night. They go home the third night

If wise guy A sees 9 then wise guy B sees 4 or 1
because wise guy B knows that if Wise guy A
saw 12 they'd gone home. On the third night Wise Guy A knows that wise guy B didn't answer so he now knows that wise guy B saw 4 the go home the fourth night

If wise guy A sees 5 then wise guy B sees 8 or 5
because wise guy B knows that if Wise guy B
saw 8 they'd gone home the forth night. Do he must have seen 5 and they go home the fifth night

Very much along the right lines, but you have the count of nights wrong, and a few typos. Looking at the question, I can see that I didn't state explicitly that the fifth evening was the fifth evening after their arrival at the castle. I'll see if I can fix it.

But I'm sure you'll be able to come up with the answer I intended, now that I've clarified the count of the nights.