My Math Forum 11 cards

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 November 9th, 2009, 12:45 PM #1 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 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.
 November 9th, 2009, 02:40 PM #2 Global Moderator   Joined: May 2007 Posts: 6,660 Thanks: 648 Re: 11 cards 1,2,4,8,16,32,64,128,256,512,1024 You can easily see the picture.
 November 9th, 2009, 06:48 PM #3 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 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.
November 10th, 2009, 04:44 PM   #4
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Re: 11 cards

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 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.

 November 14th, 2009, 11:07 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,098 Thanks: 1905 There's some leeway; the numbers could be 1, 2, 4, 8, 16, 32, 64, 125, 250, 500, 1000.

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