You have exactly $1000 in $1 bills. That's one thousand one-dollar bills. You also have a stack of empty envelopes. You will be separating the bills into different envelopes, as many envelopes as you need. Every envelope can have a different amount of money, and what's in the envelope is not secret - you can write it on the outside of the envelope if you want to before you seal it. Once your money is divided, someone will ask you for a random amount of money, between $1 and $1000, and you will hand them the envelope (s) that add up to exactly the requested amount. What is the fewest number of envelopes you need to use to make this possible, no matter how much is requested? And how many dollar bills are in each envelope?

Fewest number of envelopes 10 and 1$, 2$,$4, 8$, 16 $, 32 $,64 $ + 128,$ 256 $, 489 $

Step-by-step explanation:

Given:

$1000 bills with 1$ bill are start which remains to 999$

To Find:

Fewest number of envelopes you need And how many dollar bills are in each envelope?

Solution:

Consider first 1 $ to get total of 1000$ bills on short way is to find a series which ultimately adds up to 1000$

So using the logical that double the previous bill amount one can easily achieve

So 1st amount is of 1 $ Next will be double of 1 $ i. e 2 $

2$ to 4$, 4 $ to 8$ then 8 $ to 16 $

16$ to 32 $

32 $ to 64 $,

64 $ 128$,

128$ to 256 $

256 $ to 512 $

512 $ to 1024 $ But we started from 1 $ so it will 1023 $

But we exceeded 1000$ by 23 $ i. e.

We need to subtract the 23 $ tofrom last number,

So last nu, ber 512 $ become 512 - 23 $=489$

Hence which Form a series like as

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

Hence Total number envelope will 10

And each envelope has double the amount of previous ones with 1 $ at start.