Sum and Product Confusion Puzzle
Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.
Sam: I don’t know what the numbers are Pete.
Pete: I knew you didn’t know the numbers… But neither do I.
Sam: In that case, I do know the numbers.
What are the numbers?
assume no are a and b
As sam has sum of no a + b = x(which has given )—————(1)
and pate has produnt a*b = y(given)
now (a+b)^2 = a^2 + b^2 + 2 * a *b
find out a^2 + b^2 from above
now find a-b = sqrt(a^2 + b^2 – 2 * a *b)——————–(2)
solve (1) and (2)
n get the a and b … it depends on x(sum) and y(product)
Finally we can say if you know sum (name) and product(name) you know the number(:P)
Answer- 3 and 4.
Explanation-
As Sam knows the sum of the numbers (x + y) he would only know the answer immediately.
If the sum was 4 (2 + 2) or 5 (3 + 2),then when Pete (who knows x*y) knew that Sam didn’t know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2)
When Pete doesn’t know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2).
At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.
What if the numbers are 2 & 6? The sum would be 8, which means that the numbers could be 3 & 5 as well. (i.e., multiple pairs of numbers adding up to same result – Condition 1) The product would be 2 * 6 = 12, which is also product of 3 & 4. (Multiple pairs of numbers having same product – Condition 2)
If the sum is 8 than Sam has 3 options 2 & 6 , 3 & 5, 4 & 4 and the product that Pete can have is 12 (could be from 2*6 or 3*4), 15 (can only be from 3*5), and 16 (could be from 4*4 or 2 * 8).
So when Pete says he doesn’t know the number meaning he has more than one option so it can’t be 15 so he has 12 or 16. and in both option he could say that : “I knew you didn’t know the numbers”. But it case of 2 & 6 how does it help Sam to distinguish between 2,6 and 4 &4??
That’s why 2 & 6 is not possible!!
The numbers are 3 & 4
Explanation: If the sum was 4 (2+2) or 5(2+3) Sam would know the answer immediately. If the sum was 6 (2 &4 , 3 & 3), Pete would know the answer immediately because the product is 8 or 9 which has only one combination. So if the sum is 7 (2+5, 3+4), Sam doesn’t know the answer but is is was 2 & 5 Pete would know because the product is 10. So since he doesn’t know he has 12 so he can say he does not know the answer and also know that Sam also does not know. So that how Sam now knows the answer/
Your Answer
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