If someone was to give you one cent on Jan 1 , two cents on Jan 2nd , four on Jan 3rd and so on. i.e. keep doubling it every day. How much total money would you have collected by Jan 31?
2006-08-26 08:42:18 · 9 answers · asked by MiKe 3 in Science & Mathematics ➔ Mathematics
Just under twenty-one and a half million dollars.
On 2nd January you have a total of 3 cents, on 3rd January, you have a total of 7 cents, on 4th January you have a total of 15 cents, It is always 1 cent less than the next power of 2, so on nth January it is a total of 2^n - 1 cents and so on 31st January it is a total of (2^31) - 1 cents = 2,147,483,647 cents = $21,474,836 and 47 cents
METHOD: As I know that 2^10 = 1024, I just cubed 1024 on my calculator (and got a value for 2^30), doubled that (to make 2^31) and then subtracted one from that (to yield (2^31) -1),
2006-08-26 08:46:55 · answer #1 · answered by Anonymous · 6⤊ 0⤋
2^30 + 1 Cent = 1073741825 cents
Updated: Well, it's not that actually. That would be the amount the person would give you on the last day, 31st of January.
The correct answer is 1+2+4+8+16+...+2^30 which is calculated using the formula (a1 + an) * n/2 = (1 + 2^30) x 31/2 = 16,642,998,287.5 cents
2006-08-26 08:45:51 · answer #2 · answered by Ricardo 1 · 0⤊ 1⤋
Looking at the previous answers, I can say that a lot of them are one day short.
If you received 1¢ on Jan 1st and doubled it every day until Jan 31st, on the 31st, you would receive 1,073,741,824¢ just that day.
However, you have to remember that you're looking for the total money, not the amount received solely on that day. Add that together with everything you've already collected each day of the month, the total is actually 2,147,483,647¢, or $21,474,836.47.
You can run the test in Excel to check it. In cell A1, put 1. Then in cell A2, you use the SUM function and make it =SUM(A1*2). Then in cell A3, you put =SUM(A2*2), all the way down to cell A31 (you can drag from the lower edge of cell A3 down to cell A31, it will save the formula of "previous cell times 2"). You will see that 1,073,741,824 will be in cell A31. Then using the SUM function again, you will come up with the total amount of money received by setting cell A32 (or any other cell for that matter) =SUM(A1:A31).
2006-08-26 09:03:06 · answer #3 · answered by caysdaddy04 3 · 0⤊ 1⤋
No folks, you are giving the amount on Jan 31, not the total amount. Ricardo your formula is for consecutive integers or something, does not apply in this case. Obviously the answer is an integer.
2006-08-26 08:50:30 · answer #4 · answered by banjuja58 4 · 0⤊ 1⤋
Read the sign. You must first convert to schekels! (Rats, it's fallen down again!) Most of Y!A's messages seem to have been written by kabuki script writers. I just wasted 20 minutes trying to get past a "We're taking a breather" page only to discover it really meant the question was deleted. [EDIT] Ah, just caught one that is straightforward: "You cannot view the question at this time." Thank you for your guidance, Yamster.
2016-03-26 20:58:18 · answer #5 · answered by Anonymous · 0⤊ 0⤋
1+2^30 = 1,073,741,825 (1 billion)
Ah, yes, you guys are correct.
The number we need is 2^0(=1) + 2^1 + 2^2 + ... + 2^30
I just ran it in MATLAB and got an answer of 2.15*10^9, or 215 billion cents. That's 2.15 billion dollars.
2006-08-26 08:46:23 · answer #6 · answered by Anonymous · 0⤊ 1⤋
2^32
2006-08-26 09:29:05 · answer #7 · answered by mskbngn 1 · 0⤊ 1⤋
a common riddle, i believe the answer is something like 1 mil.
2006-08-26 08:44:48 · answer #8 · answered by Anonymous · 0⤊ 1⤋
more than I will ever see in my life time
2006-08-26 08:52:00 · answer #9 · answered by mr. Bob 5 · 0⤊ 1⤋