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November 9th, 2009, 11:45 AM   #1
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11 cards

This is very confusing to me. It really does sound like a magic trick . Please help.

A man has 11 cards, On each card, he has written a positive whole number. He then asks you to say any whole number from 1 to 2000. You tell him a number. He then chooses some of the cards he is holding and show them to you. The numbers on the cards he shows you will add up to exactly whatever number you said. This always works, for any number you say from 1 to 2000.

What numbers are on the cards?

Thank you for your help and time.
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November 9th, 2009, 01:40 PM   #2
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Re: 11 cards

1,2,4,8,16,32,64,128,256,512,1024

You can easily see the picture.
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November 9th, 2009, 05:48 PM   #3
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Re: 11 cards

Thank you mathman for your help. Can I ask what lead you to the solution? I asked that because I spent some times trying to figure some numbers that would work, but to no help.

Thanks again.
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November 10th, 2009, 03:44 PM   #4
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Re: 11 cards

Quote:
Originally Posted by alikn
Thank you mathman for your help. Can I ask what lead you to the solution? I asked that because I spent some times trying to figure some numbers that would work, but to no help.

Thanks again.
When you work with computers you get an intimate acquaintance with number bases, in particular, base 2. Here EVERY number is then represented by an expression consisting only of 0's and 1's, where powers of 2 rather than powers of 10 (usual numbers) are the underlying terms.
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November 14th, 2009, 10:07 PM   #5
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There's some leeway; the numbers could be 1, 2, 4, 8, 16, 32, 64, 125, 250, 500, 1000.
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