"I think everyone knows that old trick about doubling your money daily, even if just starting with a penny. Before a month's past you're talking millions."
It's not a trick, it's called "binary system". Meaning powers of two. Bits.
16 bits = 65536
18 bits = 262144
20 bits = 1 048 576
24 bits = 16 777 216
This means of course that it could be translated to days and pennies. However, millions of pennies are not the same thing as millions of dollars, of course. So, even with 24 days, you would have only less then 167 thousand dollars, if you start with a penny.
30 days = 1 073 741 824 pennies, which would mean
10 737 418 or more than 10 million dollars.
So, you are correct in that estimation - by the 28th day, you already have a couple of million dollars, if I calculated it correctly.
Btw, you made an 'american typo' or two. "Past" means a time in the past, and makes no sense in the context you use the word. You probably mean to say "passed". Although "has" can probably be translated to "'s", I think it's quite clumsy english in any case - it'd be way more clear, if you had said "before a month has passed".
http://americantypo.site11.com/typos
I think your point about it being an 'old trick' comes from the story of the creator of Chess. He only wanted the King to give him rice for the game, and he could have it. A chessboard has 64 squares, and the clever Chessmaster demanded to have 64 bits of rice grains. Meaning, that you put one grain of rice on the first square, and then always double the previous amount for the next square.
(Though it's probably 63 bits, because you can express two states with one bit, so it basically is a value of two (2), but it's late and I am tired, and I don't know if I thought this correctly)
So, the first square will have one grain, the next will have two, the third has four, the fourth has eight, and so on.
1 (this would not exist in computer binary system)
2 (one bit can express two values)
4 (two bits can express four values, and so on)
8
16
32
64
128
256 (eight bits can express 256 values - hence "8-bit computers")
512
1024
2048
4096
8192
16384
32768
65536 (16-bit computers had this wide registers - I remember this far)
131072
262144 (18-bit colors were used in AGA-Amigas' HAM8-mode)
524288
1048576
2097152
4194304
8388608
16777216 (24-bit color amount - this is easy to remember, palette of AGA-Amigas)
33554432
67108864
134217728
268435456
536870912
1073741824 (30 bits is already over a billion!)
..
..
9223372036854775808 (63 bits)
18446744073709551616 (64 bits - don't even ask me to put this amount to words)
Quite a lot of grain.. after thinking that the Chessmaster would be satisfied with a couple of sacks of rice, the King and his men were shocked, when they realized they had consented to paying this man more rice than existed on the planet!
Talk about cold sweat..
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