MC Frontalot is a musician, and one of his songs is a word problem that seems to me like it belongs here. If you want to listen to it instead of just reading the lyrics, a quick video search of "MC Frontalot 80085" will bring it up on YouTube. Here is the full song, copied (with permission) directly from his website:
80085
Last time I had a math class, there wasn't any internet
invented yet. That isn't on the level but I'll try to pique your interest
with half-truths and lies.
As ever, MC Frontalot feigns innocence and denies.
I won't admit it. You can't make me say it:
that I dropped Calc B more than a year before Mosaic.
Oh no now it's out, now it's shouted from the balconies:
that Frontalot's about to be engaging in some alchemy.
I'll turn a string of operands into some smut.
If that sort of thing's offensive to you keep eyes shut.
Or better yet, don't even enter, into calculator, song.
But if you're ready to be titillated, follow along.
Ready? Go. Eighty women went to the podiatrist.
Arrive: simultaneous. Soon the scene's riotous.
Nine just leave. Those in the difference persevere,
packing up the lobby very tightly, domineered
by one Sally Gorey (that's her given name)
(though her title is Reception) (and professional acclaim
is due her) ('cause she did what needed doing). And it's done:
she opened up the schedule, slotted every single one.
But, um... not many on a Friday afternoon!
All but an eighteenth of the women in the room
had to vrooooom. For each remaining patient
x-rays were taken. Then the doctor took vacation.
Why was that vacation germane to the math?
'Cause of good data policy in the office and a vast
abundance of caution on the part of our Sally:
eight backups nightly, automated, and the tally
only ever shrinking when manually deleted.
All of this occurring in the box behind reception so she needed
a full backup of that box, noons.
These weren't incremental, so her server needs ballooned.
Who deserved to flee Duluth? The doctor was in Rio
for three work weeks and another Monday just to be so
thoroughly relaxed upon return.
Have you gathered all the facts that you needed to discern?
Morning in the office, after vacatings:
out of those belonging to the original 80 ladies.
How many digital toes were in images grand total?
Your evidence so far is largely anecdotal.
And you're keen to know if any had deformity. So icky!
Ten toes per customer; this puzzle: not that tricky.
Key in your calc. Check your seven-segment indicator.
Now add my eliteness. Notice that the sum is greater
than expected. You still have to subtract
two for a pair of things Sally has that I lack.
I warned you it was kind of immature; I wasn't skirting the issue.
Still you snicker at the calculator. "Dirty! I need a tissue."
I hope this is assumed, but I will state anyway that how you reached your answer is as important as the answer itself, and just a number (even if it's the right number) is not an acceptable answer.
Answer
The answer is
already in the title: 80085.
Here are the steps to getting there:
80 women went to the podiatrist, of which 9 just leave. There are 71 left, plus Sally, so 72. All but an eighteenth had to leave, so 4 stayed (Sally and 3 patients). 3 patients times 2 feet, so we start with 6 pictures. Then, during each of the following 25 nights (Friday to Tuesday, 3 weeks), the number of images at the box behind the reception increases by 48 (8*6) and the complete reception box gets a backup in the 'backup box' at the noon afterwards. Now, the nightly increase happens 25 times, and the daily backup happens 24 times. That results in a total of 15750 images. The amount of toes is 15750*5, so 78750. Now add my eliteness, so 1337. This results in 80087. We have to subtract 2, so we end up with 80085.
And now in plain calculations:
women = 80-9 = 71
women = 71+1 = 72
women = 72/18 = 4
patients = 4-1 = 3
pictures = 3*2 = 6
reception(1) = 54, backup(1) = 54
reception(2) = 102, backup(2) = 156
reception(3) = 150, backup(3) = 306
reception(4) = 198, backup(4) = 504
reception(5) = 246, backup(5) = 750
reception(6) = 294, backup(6) = 1044
reception(7) = 342, backup(7) = 1386
reception(8) = 390, backup(8) = 1776
reception(9) = 438, backup(9) = 2214
reception(10) = 486, backup(10) = 2700
reception(11) = 534, backup(11) = 3234
reception(12) = 582, backup(12) = 3816
reception(13) = 630, backup(13) = 4446
reception(14) = 678, backup(14) = 5124
reception(15) = 726, backup(15) = 5850
reception(16) = 774, backup(16) = 6624
reception(17) = 822, backup(17) = 7446
reception(18) = 870, backup(18) = 8316
reception(19) = 918, backup(19) = 9234
reception(20) = 966, backup(20) = 10200
reception(21) = 1014, backup(21) = 11214
reception(22) = 1062, backup(22) = 12276
reception(23) = 1110, backup(23) = 13386
reception(24) = 1158, backup(24) = 14544
reception(25) = 1206
totalimages = 1206+14544 = 15750
toes = 15750*5 = 78750
elitetoes = 78750+1337 = 80087
answer = 80087-2 = 80085
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