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Solution to Puzzle 97.  BALANCE

 

Let R, B, G, X be the weights of the red, blue, green and gray objects respectively.  From the figures, we have the following equations:

(1)  2*(B+R) = B+G

(2)  2*X = R + X + G

(3)  4*R = B + X

Combining equations (2) and (3) yields

(4)  3*R = B+G

Combining equations (1) and (4) yields

          2*B = R

Since the length of level on left side is twice that on the right side, only one red weight is needed to counter balance the blue weight on the left side.

 

 

 

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The Last Recreations:  Hydras, Eggs, and Other Mathematical Mystifications

Author:  Martin Gardner

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