You have 4 weights weighing 2,3,5 and 7 pounds. The problem is none of them are marked. What is the fewest number of weighings you need using a balance scale figure out which weights are which?
My son asked me a riddle yesterday. I answered it to his shock and posed this puzzle to him. I told him that it could be done in 4, but may take 5. Five minutes later he came to me and asked why it would take more than 4. Here is his solution:
1st weighing: Weigh 2 weights against the other 2. The heavier side must have the 7 on it. Call the two lighter weights A and B.
2nd weighing: Weigh the other two against each other. Label the heavier on 7 and the lighter one C.
3rd weighing: Weigh A and B against the 7. There are 3 possibilities. A and B = 7, A and B > 7, or A and B < 7.
4th weighing: Weigh A against B.
If A and B = 7 then the lighter of A and B will be 2 and the heavier will be 5 leaving C as 3.
If A and B > 7 then the lighter of A and B will be 3 and the heavier will be 5 leaving C as 2.
If A and B < 7 then the lighter of A and B will be 2 and the heavier will be 3 leaving C as 5
My son's solution
