32 card trick
Alfred, Brian, Christopher and Damon play with a deck of 32 cards. Damon deals them out unequally, then says: "If you want us to have the same number of cards, do exactly as I say. You, Alfred, divide half of your cards between Brian and Christopher. Then, Brian, you do the same with Christopher and Alfred. Finally, Christopher, you follow suit with Alfred and Brian." How did Damon distribute the cards?
Labels: mathschallenge
posted by Chris at
6:49 PM
2 Comments:
A+B+C+D = 32
Since Damon is unaffected by the procedure, he must have gotten the right number of 8 cards.
Working backwards:
A3=8
B3=8
C3=8
C2 = C3*2 = 16
B2 = B3 - C2/4 = 4
A2 = A3 - C2/4 = 4
B1 = B2*2 = 8
A1 = A2 - B1/4 = 2
C1 = C2 - B1/4 = 14
A0 = A1*2 = 4
B0 = B1 - A0/4 = 7
C0 = C1 - A0/4 = 13
The initial distribution was A=4, B=7, C=13, D=8
Well done Ross. First post and you did it a ToM way.
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