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How Many Marbles?
 
Q Marta distributed 100 marbles among five bags.

Bag #1 and Bag #2 together contain 52 marbles.
Bag #2 and Bag #3 together contain 43 marbles.
Bag #3 and Bag #4 together contain 34 marbles.
Bag #4 and Bag #5 together contain 30 marbles.

How many marbles are there in each bag?
 

 
A Bags #1, #2, #4, and #5 together contain 82 marbles. Therefore, Bag #3 must contain 18 marbles. With that piece of information, you can figure out how many marbles the other bags contain:

You know Bag #2 and Bag #3 = 43 marbles; you know Bag #3 = 18 marbles; therefore, Bag #2 contains 25 marbles.

You know that Bag #1 and Bag #2 = 52 marbles; therefore, Bag #1 contains 27.

You know Bag #3 and Bag #4 = 34 marbles; you know Bag #3 = 18 marbles; therefore, Bag #4 contains 16 marbles.

You know that Bag # 4 and Bag #5 = 30 marbles; you know that Bag #4 contains 16 marbles; therefore, Bag #5 contains 14 marbles.

From Bernardo Recamán Santos, Challenging Brainteasers: Official American Mensa Puzzle Book. New York: Sterling Publishing Co., Inc. Originally published in Colombia by Editorial Norma S.A. under the title Juegos y Acertijos para la Enseñanza de las Matemáticas.