Question

Divide $523 (in whole $ increments) into a number of bags
so that I can ask for any amount between $1 and $523 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

Step-by-step explanation:

Given that: Divide $523 (in whole $ increments) into a number of bags so that I can ask for any amount between $1 and $523 and you can give me the proper amount by giving me a certain

number of these bags without opening them.

To find: What is the minimum number of bags you will require?

Solution: These type of questions can be easily solved by keeping in mind that,one can formed any number by addition of the numbers of series

1,2,4,8,16,32...

I.e.

${2}^{0} , \: {2}^{1}, \: {2}^{2} ,\: {2}^{3} ...$

Thus here in the given question

No. of bags can be counted by writing this type of series

So,

1,2,4,8,16,32,64,128,256 and 12

Because addition of 1+2+4+8+16+32+64+128+256+12=523

Bag1: $1

Bag2:$2

Bag3:$4

Bag4: $8

Bag5:$16

Bag6:$32

Bag7: $64

Bag8:$128

Bag9:$256

Bag10:$12

Thus, total number of bags are 10.

Justification: Let us take some random number of dollars,because it is not possible to take all the numbers from

$1 to $523

$10= Bag 2 +bag4= $2+$8=$10

$150=Bag2+Bag4+Bag8+Bag10=2+8+128+12=$150

$268=Bag9+Bag10=256+12=$268

$324=Bag3+Bag7+Bag9 =4+64+256=$324

$413=Bag1+Bag5+Bag8+Bag9+Bag10

= 1+16+128+256+12=$413

By this way all the denominations from 1 dollar to 523 dollar will be given from these 10 bags.

Hope it helps you.