May 08, 2021
RAY: 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 configure those 10 envelopes, that is, 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."
RAY: I gave Tommy a thousand $1 bills, and his assignment was, first, come up with 10 envelopes, and once he did that he had to figure out a way to put various numbers of dollar bills in those 10 envelopes so that no matter what amount of money I asked him for, he could hand me some combination of envelopes and always be sure of giving me the exact right amount. The question is: How did he do it?
That's the question, you thought the question was, “What was going on in your mind that you gave me 1,000 $1 bills?”
I could've given a hint last week and said one of the envelopes has $489 in it.
And the other nine have $1, $2, $4, $8, $16, $32, $64, $128, and the ninth envelope has $256. If you add those up -- 256, 128, 64, 32 -- you come up with 511, because in base 2, the next number would be…
512, OK? Two to the tenth would be 512, but he couldn't put 512 because you don't have it in there.
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, and da-da-da.
Pretty good, huh? Give me my thousand bucks back. It was only a loan.
You can't do it unless the number is two. There you go, see? The power of two. Right?