Person 1 was given a set of 5 cards numbered 1 to 5, and person 2 was also given a set of 5 cards numbered 1 to 5. They were then blindfolded and told to pick a card from their respective sets.

The sum of the numbers from the two cards was told only to person 1 and the product of the numbers was told only to person 2. They were then told to name the numbers on the two cards they had chosen. Below is what each of them said.

2: I don’t know the two numbers.

1: Now I know the two numbers.

2: I still don’t know the two numbers.

1: Let me help you. The number I was just told is *larger* than the number you were just told.

2: Now I know the two numbers!

So, what were the two numbers?

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