It's All Fun And Games
One day, Claire was bored and decided to play a little experiment with her two friends--Danielle and Erica--. Claire told them that she would be using exactly 2 numbers out of the 4 numbers: 4, 5, 6 and 7.
Claire then, separately, told Danielle the sum of the two numbers and told Erica the product of the two same numbers.
Then unbeknownst to us, either Danielle or Erica made the assertion: "I don't know what the 2 numbers Claire chose."
If everyone is perfectly logical and speaks the truth, can we as the reader determine who made this assertion?
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1 solution
Try multiplying the numbers together.
4x5=20 5x6=30 6x7=42
4x6=24 5x7=35
4x7=28
Each product is different therefore Erica can figure it out. The sums of the numbers are not as distinct.
4+5=9 5+6=11 6+7=13
4+6=10 5+7=12
4+7=11
If Clare said the sum is 11 then Danielle has no way of knowing if the numbers are 4 and 7 or 5 and 6