[math-fun] Cute Puzzle: What Are The Two Numbers?
The puzzle is from the Winter 2000 issue of The Bent of Tau Beta Pi: www.tbp.org/pages/Publications/Bent/BTs/W00.pdf There are two integers, A and B, which are integers greater than 1 and less than 101. Neither Sam nor Pete knows what they are, but Sam knows their sum, and Pete knows their product. The following conversation takes place. Pete: “I don’t know what the numbers are.” Sam: “I knew that you did not know what the numbers are.” Pete: “Now I know what the numbers are.” Sam: “Then, so do I.” What are the values of A and B? — Don Holden ----- The solution is here: www.tbp.org/pages/Publications/Bent/BTs/Sp00.pdf
On 3/1/08, Robert Baillie <rjbaillie@frii.com> wrote:
The puzzle is from the Winter 2000 issue of The Bent of Tau Beta Pi: www.tbp.org/pages/Publications/Bent/BTs/W00.pdf
There are two integers, A and B, which are integers greater than 1 and less than 101.
Neither Sam nor Pete knows what they are, but Sam knows their sum, and Pete knows their product.
The following conversation takes place.
Pete: "I don't know what the numbers are." Sam: "I knew that you did not know what the numbers are." Pete: "Now I know what the numbers are." Sam: "Then, so do I."
What are the values of A and B? — Don Holden ----- The solution is here: www.tbp.org/pages/Publications/Bent/BTs/Sp00.pdf
I'm afraid the bound A,B < 101 is too high: an alternative solution overlooked by the setter is A = 4, B = 61 [and I think I also know the reason he missed it]. WFL
On 3/1/08, Fred lunnon <fred.lunnon@gmail.com> wrote:
I'm afraid the bound A,B < 101 is too high: an alternative solution overlooked by the setter is A = 4, B = 61 [and I think I also know the reason he missed it].
WFL
Oops --- apologies in order. In fact, the given bound is unnecessarily low: I find A,B < 219 still gives a unique solution! WFL
participants (2)
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Fred lunnon -
Robert Baillie