Alzim and Era each select a whole number greater than zero and play a game.
Mufti, the host of a part of logicians, says, “Each of you has picked a whole number greater than zero and secretly reported the number to me. I have written the sum of the numbers on one card, and the product on another card. I have randomly hidden one card and will reveal the other.”
Mufti reveals a card showing the number 2020, and asks, “Do you know the other person’s number?” Alzim and Era are asked this in turn.
Alzim replies, “No, I do not know Era’s number.”
Era says, “No, I do not know Alzim’s number.”
Then Alzim replies, “Yes! I know Era’s number!”
So what was Era’s number? And what can you conclude about Alzim’s number?
