A penny a day

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Dragginourbedaround

Dragginourbedaround

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There are a lot of smart people on this forum so this is probably a no brainer but, what would be your response if you were given 5 minutes to decide whether or not to work a 30 day contract for a penny a day doubled every day?  No calculators.

 
Sign me up, that's a whole lot of pennies and pennies add up to be dollars...
 
I'll take it.  If it starts doubling on the second day that is over $5M dollars.

Mike.
 
It starts off slowly but toward the end of the month the $/day becomes huge!  But these days you might be laid off by Day 15, so maybe better to ask for a fixed rate of pay...
 
I would take the job.. 2^30 is a very impressive number...

The classic puzzle however is this

You are offered two 30 day contracts
One pays 100/day for 30 days
The other pays only 1? for the first day but every day they double it (second 2? 3rd day 4?)

Which job should you take.

Answer "The other" (The penny a day doubled daily for 30 days)

Puzzle was featured on Walker Texas Ranger by the way.. Of course the street smart kit took the first,, Walker showed him the value of thinking.
 
It's a lot more than 2^30 (for a 31 day month).  The formula is:

SUM(2^x) x=0 to n-1 where n is the number of days in the month.
 
Ahhh.. A trick question.
A lot depends on if you get paid in pennies or dollar bills at the end of the month.
Make sure to get pennies.
536,870,912 pennies weigh 1,677.5 tons
At the current price of copper, you could melt them down (illegal of course, but for the sake of argument) and turn your $5,368,709.12 into $12,231,440.93
 
It's actually 2,147,483,647 pennies after 31 days, so it's 4 times as many, Bob.  Good luck in hauling that much weight to the smelter :)
 
Ned, I've got nothin' to do waiting for the thaw, so I hereby challenge your math.  ;D
Maybe I'm off (wouldn't be the first time). I'm an excel junkie.
"1" in cell A1
"2" in cell A2
A3 = A2*2
'Fill down' A3 to A30
gives us 536,870,912
Did I screw it up somewhere? Or do you owe me lunch?  ;D ;D
 
My figures (for 2^31) match Ned's -- (2,147,483,648 - 1). For 30 days, of course, it's (1,073,741,824 - 1), which matches the puzzle John referred to (it's a lot older than Walker Texas Ranger John). The Windows (Win 7) calculator makes that easy, though I have more than one handheld calc that gives the same result.
 
oh oh.... I feel a thrashing coming on...... :-[

Where was my error in Excel? Each day duplicated doubled the previous day. This may just drive me crazy....
 
Add up all the day value.  See my  fourth formula above.
 
Still don't see it Ned.
If I earn a penny on day one, two pennies on day two, four pennies on day three, and so on thereby doubling the previous day......

1
2
4
8
16
32
64
128
256
512
1,024
2,048
4,096
8,192
16,384
32,768
65,536
131,072
262,144
524,288
1,048,576
2,097,152
4,194,304
8,388,608
16,777,216
33,554,432
67,108,864
134,217,728
268,435,456
536,870,912

$5,368,709.12
 
Now add all those up.  Larry used the shorter method, but I used a formula that reflected the problem as stated.

SUM(2^x) x=0 to n-1 where n is the number of days in the month = (2^n)-1
 
Doh!  I forgot to add the little buggers up!
As Jimmy Stewart said in "Flight of the Phoenix"..... "Engineers will take over the world someday."
Thanks for a bit of afternoon entertainment.  ;D
Looks like I owe Ned lunch......
 
It was refreshing dusting off some long time unused math knowledge.

I'm up for lunch :)
 
Ned said:
It's a lot more than 2^30 (for a 31 day month).  The formula is:

SUM(2^x) x=0 to n-1 where n is the number of days in the month.
Click to expand...

I know but just the 31st day is a staggering sum  The person who calced it out cam up with just shy of 5 BILLION.

Or about what hackers cost us every short period of time.

Walker showed the numbers too in the TV show.. Which was a 2 parter where he set up a "Boot Camp" type operation for troubling teens.  The guy who played LINK on Mod Squad was observing for the Atty General and he was very much against the program, At the end of the 2 parter.. He takes over for walker when the second group of "Volunteers" arrive.  Seems he was converted.
 
    Of course you all realize that Canada is always trying to be a bit different, and the answer north of the border would be ZERO.  The penney is no longer legal currency in Canada, so, no matter how many times you double it, it will end up at ZERO.  :(

Ed
 
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