# 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.

Relevance

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 + 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.

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