One of our newest members came up with this puzzle invloving some “epistemic trickery”.
Can you tell what do you know that he knows that you know? 
Problem #10: Some Sum Puzzle
(by Vsotvep)A teacher is testing his best students Albert, Bernard and Cheryl with a little game. He glued a piece of paper with a number written on it on each of their foreheads and told them that one of their numbers is the sum of the other two numbers, and that each of the numbers are between 1 and 5. The students can’t see their own foreheads, but they can see each other.
After the explanation the teacher asks Albert if he knows what number he has, to which Albert responds “No sir, but I know that Bernard also doesn’t know it”. The teacher then turns to Cheryl and asks whether she has the largest number or not. Cheryl, smart as she is, thought for a few seconds and declared “I didn’t know it before Albert answered your question, but I do know it now whether I’m the largest or not!” and then she proceeded to write the answer on a piece of paper which she showed only to the teacher.
- What did Cheryl write on the piece of paper?
Bonus round:
During lunch break Diana, friend of Bernard’s, told him that she’d been eavesdropping the conversation, but that there was something still bugging her. “What was going on?” she asked. "Well," Bernard responded, “if you had lined us up in alphabetic order, you could have moved one of us towards the front of the line and get the numbers in ascending order”. Somehow, Diana was satisfied with this answer.
- What were the numbers on their foreheads?
Please remember not to spoil the answer (read the first post), you can send a Private Message to the puzzle creator instead. Discussion is otherwise encouraged.