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?
(In reply to
re: 2 weighings, re(4): done in 3 weighings.... I think =P by Vina)
in 2 weightings:
first weighting
I take two weight casually, and have this results:
2 3 Tot 5. others are 5 and 7
2 5 Tot 7 others 3 and 7
2 7. Ecc. Ecc.
3 5
3 7
5 7
All of this go to 3 cases, and I can recognize the weight I have i a couple. Now I have to distinguish the weights inside the couple for both two couples. I write first the 2 value that a weight can assume:
second weightings:
I take a weight for each of two couples, put togheter and I weight. In the first case I have this results:
2+5. 7
2+7. 9
3+5. 8
3+7. 10
Also in other case I find different result.
If, like in the first case, the sum is 7, and knowing that the weights are 2 o 3 or 5 o 7 => the first is 2 and the second is 5 (unique solution that work in all the cases) => the other are 2 o 3 or 5 o 7 by esclusion the first is 3 and the second is 7 .
This work because every sum of every couple of number taken by 2,3,5,7 is different.
re(2): 2 weighings, re(4): done in 3 weighings.... I think =P
