Here is an unusual problem involving weights and balance scales. It was invented by Paul Curry, who is well known in conjuring circles as an amateur magician.
You have six weights. One pair is red, one pair white, one pair blue. In each pair one weight is a three times heavier than the other but otherwise
appears to be exactly like its mate. The three heavier weights (one of
each color) all weigh the same. This is also true of the three lighter weights.
Your aim is to determine which is the heavier weight of each pair. But wait, you can only use a balance scale (physical balance) only two times. Can you solve this? Think before you look at the solution. Sometimes easy problems are not as easy as they seem.
Solution:
First of all let us call the red weights R1 and R2, the blue weights B1 and B2 and the white weights as W1 and W2. From the problem statement it is sure that one of R1, R2 is of weight x and the other of weight 3x. Similarly for B1, B2 and W1, W2.
Weigh R1W1 with B1W2.
Case 1: If balance shows they are equal then we understand that one of R1 and B1 is heavier and the other 8s lighter (since one of W1, W2 is heavier and the other is lighter)
Now individually weigh W1 and W2. If W1 > W2, then W1 = 3x, W2 = x, R1 = x, R2 = 3x, B1 = 3x, B2 = x.
If W1 < W2, then W1 = x, W2 = 3x, R1 = 3x, R2 = x, B1 = x, B2 = 3x.
Case 2: If R1W1 > B1W1 then clearly the only possibility satisfies is that R1 = W1 =3x & B1 = W2 = x. Now R2 = x and B2 = 3x.
Case 3: If R1W1 < B1W1 then clearly the only possibility satisfies is that R1 = W1 =x & B1 = W2 = 3x. Now R2=x and B2 = x.
We are done! We have used balance scale only twice and successfully distinguished the weights of same appearance! Thanks for reading. For more support Mathhexagon. Share this post and follow me on social platforms.
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