Given two integers x,y larger than 1. S knows the sum s=x+y but not the product p=xy and P knows the product p=x y but not the sum. Now there is the following dialog: P: ``I don't know x,y", S: ``I don't know x,y". P: ``I now know x,y". S: ``I now know x,y". What are the integers? |
TRY TO SOLVE THE PROBLEM FIRST! |
Solution: Because P does not know x,y, there are more than one possible factorizations. The smallest is 12 = 6*2 = 3*4. Their sum is 8 or 7. If the sum was 7, then S could figure out the numbers. So it is not 7. P knows now that the sum had to be 8 and so that x=6, y=2. |
Given two integers x,y>1. S knows s=x+y but not p and P knows p=x y but not s. Now there is the following dialog: P: ``I don't know x,y". S: ``I don't know x,y". P: ``I don't know x,y". S: ``I don't know x,y". P: ``I now know x,y". S: ``I now know x,y". What are the integers? |
Prove that the above riddle is the hardest dialog riddle of that type. |
A student ask his teacher: how old are your 3 daughters? Teacher: ``if you multiply, you get 36. If you add, you get your house number." The student protests that it can not be solved. The teacher: ``You are right, the oldest plays the piano." How old are the daughters? |
Look at all the products. We have 6*6*1 = 36*1*1 = 18*2*1 = 6*2*3 = 4*3*3 = 9*2*2 with sums 13,38,21,11,10,13. The sum is ambiguous for 6*6*1 and 9*2*2. The last information gives 9,2,2. |