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| Marble Muse (Posted on 2014-06-23) |
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At the outset, each of the five friends Ade, Ben, Cal, Dan and Ethan had a positive integer number of marbles.
If Ade gave one-half of his marbles to Ben, and Ben gave a one third of what he then held to Cal, and Cal gave a quarter of what he then held to Dan, and Dan gave one fifth of what he then held to Ethan who then passes on a sixth of his holding to Ade - they would all have an equal number of marbles.
What is the minimum number of marbles that each of the five friends had at the beginning?
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Submitted by K Sengupta
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Rating: 4.5000 (2 votes)
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Solution:
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(Hide)
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A starts with 96, passes 48, and ultimately receives 12, ending with 60.
B starts with 42, receives 48, passes 30, ending with 60.
C starts with 50, receives 30, passes 20, ending with 60.
D starts with 55, receives 20, passes 15, ending with 60.
E starts with 57, receives 15, passes 12, ending with 60.
For an explanation, refer to the analytic solution
submitted by Steve Herman in this location. |
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