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 2006-01-23 18:03:59