# Ten Envelopes

I’m going to give you a thousand \$1 bills. You come up with 10 envelopes.

Here’s your assignment: Figure out a way to put various numbers of dollar bills in those 10 envelopes, so that no matter what amount of money I ask you for, you can hand me some combination of envelopes and always be assured of giving me the correct amount of cash.
If I say, “Give me \$637,” you can say, “oh, that will be envelope number one, envelope number six, and envelope number two.”

Can it be done? If so, Tell the RiddleDude the amounts in each envelope.

### 6 guesses to Ten Envelopes

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• Chandramouli

1,2,4,8,16,32,64,128,256 & 512

• Very close, Chandramouli.

You’re on the right track, using Base 2.

Check your math and get back to me.

• Melody

1,2,4,8,16,32,64,128,256,and 489

• Dude

Correct Melody.

The first of the envelopes has \$489 in it, the other envelopes have \$1, \$2, \$4, \$8, \$16, \$32, \$64, \$128, and \$256.
If you add those up: 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1, you come up with 511, because in base 2, the next number would be 512.

Two to the tenth would be 512, but you canâ€™t put 512 because you don’t have it. So you could put 489. So you can get any possible number between one and 511 by using the first nine envelopes, and then anything beyond 511 up to a 1,000 using 489 plus one gives you 490, 490 plus two gives you 492, etc.

You are today’s winner.

• ben

1)1
2)2
3)2
4)6
5)19
6)50
7)120
8)200
9)300
10)300

• michael brunt

put one thousand in all of them