Divide $1078 (in whole $ increments) into a number of bags so?

Question

that I can ask for any amount between $1 and $1078, and you can give me the proper amount by giving me a certain number of these bags without opening them. What is the minimum number of bags you will require?

Answer 1

Eleven. 1 + 2 + 2 + 4 + 8 + 17 + 34 + 67 + 135 + 269 + 539 = $1078.

Answer 2

539 269 134 67 33 16 8 5 4 2 1

11 bags

Answer 3

1078

Answer 4

Start with one bag that has half the amout: 539

Take 1 coin out of the remainder and put it in a bag by itself: 1

Make a bag with half of that: 269

Take 1 coin out of that one: 1

Make a bag with half of that: 134

Make a bag with half of that: 67

Take 1 coin out of that one: 1

Make a bag with half of what is left: 33

Take 1 coin out: 1

Half of what is left: 16

Half of that: 8

Half of that: 4

Half of that: 2

Half of that: 1

You have 1 left. Take it and the other 4 coins that had to be taken out and make a bag of 5.

539, 269, 134, 67, 33, 16, 8, 4, 2, 1, 5

This accounts for all the coins and it can be used to make every single amount from 1 to 1078.