Blind Cards
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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1 solution
As person 2 gets told the product, and doesn't know what the numbers are straight away, the product must have a couple of different ways of making it with the numbers 1 to 5. The only product which has 2 ways is 4, giving the possibilities 1 & 4, or 2 & 2. Person 1 will deduce this, and know what the 2 numbers are since the sum of each possibility comes to different things. Then, we are told that the sum is larger than the product. Since 5 > 4 (and 4 > 4 isn't true), the numbers must be 1 & 4.