1.

Quacky found a paper in which product of two non-zero digits(1 to 8) is given. Similarly, Mario got sum of the same two numbers and then they are having a conversation. 1. Quacky says "I don't know the numbers".Mario says "I don't know the numbers". 2. Quacky says "I don't know the numbers".Mario says "I don't know the numbers". 3. Quacky says "I don't know the numbers".Mario says "I know the numbers". What is the product of the numbers ?

Answer»

6
8
12
16

Solution :As quacky didn't come to know after knowing the product, then there will be atleast 1more pair of numbers having the same product. Possibilities are :
1x4 = 2x2
1x6 = 2x3 
1x8 = 2x4 
2x6 = 3x4 
2x8 = 4x4
3x8 = 4x6
After this MARIO tells he doesn't know, that means there are atleast two pair remaining inthe possibilities with the same sum:
1 + 4 = 2 + 3
2 + 8 = 4 + 6
2 + 6 = 4 + 4
1 + 6 = 3 + 4 
1 + 8
3 + 8
2 + 2 
2 + 4
Now in these 8 there are​​ STILL 2pairs with same product.... 
1x6 = 2x3
2x6 = 3x4
2x8 = 4x4 
1x4 
4x6
Now in the 6 there are atleast 2 PAIRS with same sum... 
1 + 6 = 3 + 4 
2 + 6 = 4 + 4 
2 + 8
2 + 3 
Now there are atleast 2 pairs with same sum... 
2,6 3,4
1,6
4,4
The product of the possibilities is 12 which will be the answer


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