Tell me something I don't know
Barry chose two not necessarily distinct integers from 1 to 6 inclusive.
He told Gerry only the sum of these two integers, and Harry only the product.
But Barry let both Gerry and Harry know that the numbers came from 1 to 6 inclusive.
The following conversation occurs:
Gerry: "I don't know the numbers."
Harry: "I don't know the numbers."
Gerry: "I don't know the numbers."
Harry: "I don't know the numbers."
Gerry: "Now I know the numbers!"
What is the product of these two numbers?
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1 solution
idk: I don't know the numbers
ik : I know the numbers.
Gerry has Sum(S) and Harry has Product(P).
Given statements:
Gerry: idk
Harry: idk
Gerry: idk
Harry: idk
Gerry: ik
Both have ambiguous product and sum as it is quite clear from their first statement. From Harry first idk statement, possible products might be :
4 = 1 x 4 = 2 x 2;
6 = 1 x 6 = 2 x 3;
12 = 2 x 6 = 3 x 4;
From these possible products, Harry may have the sum of one of the sum of the above factors which are:
i) 4 = 1 + 3 = 2 + 2;
ii) 5 = 1 + 4 = 2 + 3;
iii) 7 = 1 + 6 = 3 + 4 = 2 + 5;
iv) 8 = 2 + 6 = 1 + 7 = 3 + 5 = 4 + 4;
Now creating cases what Gerry might have:
CASE 1:
Sum = 8 (2, 6) (1, 7) (3, 5) (4, 4)
Product(P) = 12 7 15 16
Possible cases for : (2, 6) S = 8 (1, 7) (3, 5) (4, 4)
product (3, 4) S = 7
This is what the conversation would be:
Gerry: idk (as so many possible numbers)
Harry would say "ik" if P = 7, 15 or 16 as these numbers are unique to find. but given statement is "idk" that means Gerry would be able to identify P = 12 and the combination. Therefore the next statement be like :
Harry: idk
Gerry: ik
As this conversation do not resemble the given statements. This will not be the case i.e. Sum not equal to 8 but P can be 12.
CASE 2:
Sum = 7
(1, 6) (2, 5) (3, 4)
P = 6 10 12
Possible cases for P = (1, 6) S = 7 (2, 5) (3, 4) S = 7
(2, 3) S = 5 (2, 6) S = 8
Gerry: idk (many possible numbers)
Next Harry would say "idk" that means P != 10.But that doesn't give any clue to Gerry so he say "idk" but this statement is very important as it involves critical analysis of above and next few cases.
Answer : Product is 6 . My time is up right now. I will complete the solution sometime later.