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 I Only Need Two - Part II (Posted on 2006-01-23)
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?

 Submitted by Vernon Lewis Rating: 4.2500 (4 votes) Solution: (Hide) Thanks to Brian Smith for the original problem and to Leming for the improved solution. Separate the stacks into two piles of 6 and one of 5 coins. 1. Weigh the two stacks of 6 coins against each other. Label the heavier stack "A", the lighter stack "B" and the stack of 5 coins "C". The 35g coins will be 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 will have 3, 4, or 5 35g coins unless If A balanced with B and heavier than C or If A heavier than 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: i. Weigh 3 vs 3. The heavy (or balanced side) will have at least two 35g coins. Keep the heavy stack. ii. From the heavy stack of three coins weigh 1 vs 1. If they are balanced both are 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. ii. Unbalanced: The heavy side will have two 35g coins. Weigh 1 vs 1 as above to find the two coins. Total: 4 Weighings ii. 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

 Subject Author Date Solution (spoiler) Leming 2006-01-23 18:03:59

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