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The Difference Scale (Posted on 2005-07-01)

You have a scale which compares two weights but instead of telling which is heavier or lighter, this scale returns the difference of the weights but will not tell which is heavier. In order for the scale to display an accurate result, the amount of weight on each side must be at least 20g and the difference can not exceed 20g. The scale will not report a result unless there is a weight on each side. If the difference exceeds 20g, the scale will report an error.

Use this scale no more than six times, sort an otherwise identical set of six coins with weights of 20, 21, 22, 23, 24, and 26 grams.

Examples:
Ex 1: If A=30 B=30 then the scale reports 0 (equal)
Ex 2: If A=31 B=29 then the scale reports 2
Ex 3: If A=29 B=31 then the scale reports 2 (undistinguishable from example 2)

Submitted by Brian Smith

Rating: 4.3333 (3 votes)

Solution: (Hide)

Choose one coin (X) and compare it to all five other coins
Case 1: The differences are 1,2,3,4,6
Coin X is 20g and the coins with differences 1,2,3,4,6 are 21,22,23,24,26g respectively.
Case 2: The differences are 1,1,2,3,5
Coin X is 21g, the coins with differences 2,3,5 are 23,24,26g respectively. The two coins with difference 1 are 20g and 22g. Compare one against the 26g coin to find out which.
Case 3: The differences are 1,1,2,2,4
Coin X is 22g, the coin with difference 4 is 26g. The two coins with difference 1 are 21g and 23g, call them A and B. The two coins with difference 2 are 20g and 24g, call them C and D. Compare pairs of coins (22g+26g) against (A+C).
Diff. Coins
1 A=23, B=21, C=24, D=20
3 A=21, B=23, C=24, D=20
5 A=23, B=21, C=20, D=24
7 A=21, B=23, C=20, D=24
Case 4: The differences are 1,1,2,3,3
Coin X is 23g, the coin with difference 2 is 21g. The two coins with difference 1 are 22g and 24g, call them A and B. The two coins with difference 3 are 20g and 26g, call them C and D. Compare pairs of coins (23g+21g) against (A+C).
Diff. Coins
0 A=24, B=22, C=20, D=26
2 A=22, B=24, C=20, D=26
4 A=22, B=24, C=26, D=20
6 A=24, B=22, C=26, D=20
Case 5: The differences are 1,2,2,3,4
Coin X is 24g, the coins with differences 1,3,4 are 23,21,20g respectively. The two coins with difference 2 are 26g and 22g. Compare one against the 20g coin to find out which.
Case 6: The differences are 2,3,4,5,6
Coin X is 26g and the coins with differences 2,3,4,5,6 are 24,23,22,21,20g respectively.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Another way	Rupesh Khandelwal	2005-07-04 11:30:14
re: Solution	Stefanie Mason	2005-07-02 03:32:58
Solution	josh	2005-07-01 17:33:00
Idea	Lisa	2005-07-01 14:29:16

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