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The Color Problem

Q. You are not called upon to test your skill in the game of cards. It is merely a color problem.

Take a pack of playing cards. You know they are 52 in all. Separate the red from the black. Now give it to me, I have arranged them as under:

Pile No. 1: There are three times as many blacks as red.

Pile No. 2: There are three times as many red as black.

Pile No. 3: There are twice as many blacks as red.

Now, could you tell number of cards of each color in each of the three piles?

A. The lead equation x = 5y = 26 tells you that cannot be less than 6 (otherwise you couldn’t subtract 26 from 5y). The suggested second equation will yield z=52-8y, which means that y cannot be more than 6. If it can be neither more than nor less than 6, it must be 6. From our first equation above this makes x=4, and from the second, z=4. The rest is easy.

(Pile 1) 12 Blacks and 4 Reds.
(Pile 2) 6 Blacks and 18 Reds.
(Pile 3) 8 Blacks and 4 Reds.