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Friday Riddle

nudgie's picture
Posts: 1483
Joined: Sep 2006


RIDDLE: You manufacture brain wave entrainment CDs for companies that sell self-improvement products. You are at the post office, with ten boxes of them ready to close up and ship out, but you have a problem. Nine of the boxes contain CDs that are designed to put the listener into an "alpha" or relaxing state, and one is full of Cds that are designed to put the user into a deeper "delta" state, for deep sleep. They look identical, and you forgot to label them.

There is one difference, however. You remember that the "alpha" Cds weigh 13 grams, and because different CD "blanks were used, the "delta" Cds weigh 15 grams. Unfortunately, you can't feel the difference in weight by lifting them.

The post office does have a scale. It costs one dollar each time you weigh something, though, and you want to keep your costs down. How do you use the scale as few times as possible to determine which are the "delta" CDs?

PhillieG's picture
Posts: 4905
Joined: May 2005

My advice would be to listen to the CD's and improve your brain waves so you would not forget to label them!

I do not believe anyone will get this without Googleing but that never stops some people ;-)

Posts: 62
Joined: Jul 2009

Hmm... You split the group in half and weigh one of the groups. If the total weight is a multiple of 13, then the other group has the box of deltas. You then take the group with the box of deltas and split it in half and weight one of the groups to find the group that is a multiple of 13 so that you can eliminate that group. Continue the process until you find the box of deltas. At the most, you would only have to weigh 4 times.

Is that right?

PGLGreg's picture
Posts: 741
Joined: Jul 2006

Gather up 1 CD from the first box, 2 CDs from the second box, and so on, and weigh this pile. There will be 55 CDs in the pile, weighing 55*13 grams plus a few extra grams because of the delta CDs: 2 extra grams if the first box had the deltas, because then only one of the CDs is a delta, 4 extra grams if the second box had the deltas, and so on. So in one weighing, the box with the deltas is identified.

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