SOLUTION: I'm stuck on this word problem. A person has $1,000 and he needs to divide it into 10 envelopes so that any amount, from $1 to $1,000, can be given out by using one or a combinatio

Question 17540: I'm stuck on this word problem. A person has $1,000 and he needs to divide it into 10 envelopes so that any amount, from $1 to $1,000, can be given out by using one or a combination of 2 or more of the envelopes. Two envelopes can contain the same amount. I know you need have the smaller numbers, 1 through 9, so I have picked 1, 2, 3 and 4 for those. I also think you need $10 in one envelope and $20 in another, plus a $100 envelope and a $500 envelope. I have solved this using 12 envelopes, but not 10. Is there a formula or table I should be using to solve this? I really need your help! How does this work?
Answer by askmemath(368) (Show Source):
You can put this solution on YOUR website!
For problems like these, you need to take powers of 2 as the amount that needs to go into the envelopes,
Starting from 0
2^0 = 1 so 1 goes into the first envelope
2^1 = 2 2nd Envelope
2^2 = 4 3rd envelope
So, let's see what all amounts we have
1
2
1+2 = 3
4
4+1 = 5
4+2 = 6
4+2+1 = 7
Now if you took 2^3 for the 4th evelope you would get more amounts. However can you find out what goes into the 10th envelope??