How to divide 1000 coins in to 10 parts such that from this 10 parts able to select 1 to 1000.?

How to divide 1000 coins in to 10 parts.After dividing we should able to get any number from 1 to 1000.Example If I want 99 I should get like 50+20+20+5+2+2. Here I have selected 6 parts. Like this should able to get any number from 1 to 1000 by selecting some parts.

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  • 1 decade ago
    Favorite Answer

    Just use powers of 2:

    1, 2, 4, 8, 16, 32, 64, 128, 256, and the last one must be 489.

    Whatever number from 1-1000 you want to make up, just continually choose the largest possible number and use that (its just like writing the number in binary).

  • 1 decade ago

    1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 489 = 1000

    For the amounts up to 511, you just use combinations of 1 through 256, much like binary counting.

    For example:

    1 = 1

    2 = 2

    3 = 2 + 1

    4 = 4

    5 = 4 + 1

    6 = 4 + 2

    7 = 4 + 2 + 1

    8 = 8

    9 = 8 + 1

    ...

    For amounts 512 or above, just subtract 489 and then do the remainder as before:

    512 = 489 + 16 + 4 + 2 + 1

    513 = 489 + 16 + 8

    514 = 489 + 16 + 8 + 1

    515 = 489 + 16 + 8 + 2

    etc.

    The set is basically powers of two. Normally the last pile would be 512, but this question asks for a division of 1000 (rather than 1023, so it is 23 coins smaller --> 512 - 23 = 489). It still works.

  • 1 decade ago

    1,2,4,8,16,32,64,128,256 and the rest: 489

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