In
I Only Need Two, you have 12 30g coins, 5 35g coins and a balance scale. As shown previously you can identify 2 of the 35g coins with 4 weighings. How many weighings are required if the scales can only weigh a maximum of 6 coins per side?
(Usually 4, sometimes 5)
Limited to 6 coins per side . . . separate the stacks into piles of 6, 6, and 5 coins.
1. Weigh the two stacks of 6 coins against each other. Label the heavier stack "A", the lighter labeled "B" and the stack of 5 coins "C".
The 35g coins should be organized as one of these combinations:
A B C
5 0 0
4 1 0
4 0 1
3 2 0
3 1 1
3 0 2
2 2 1
2 1 2
1 1 3
1 0 4
0 0 5
Take one coin from B and add it to C.
2. Weigh A vs C. Keep the heavier of A and C. The heavier stack should have 3, 4, or 5 35g coins. (Exception: 1. If A balanced with B and outweighed C or 2. If A outwieghed B and balanced with C. Then there are only two coins in the heavy stack.)
3. With 3, 4, or 5 heavy coins out of 6:
a. Weigh 3 vs 3. The heavy (or balanced side) will have at least 2 35g coins. Keep the heavy stack.
b. From the heavy stack of three weigh 1 vs 1. If they are balanced they are both heavy. If one is heavier than the other, then that coin and the one not weighed are the two 35g coins.
Total: 4 Weighings.
4. With 2 heavy coins out of 6:
Weigh 3 vs 3.
a. Unbalanced: The heavy side will have two 35g coins. Weigh 1 vs 1 as above to find the two coins.
Total: 4 Weighings
b. Balanced: Each side has one heavy coin. Take one stack and weigh 1 vs 1. If these balance the heavy coin is the 3rd of the three. If unbalanced the heavy side is the 35g coin. Repeat for the other stack of 3.
Total: 5 Weighings

Posted by Leming
on 20060123 18:03:59 