Kory Math Problems
My friend Kory sends me math problems every so often, and I send him some too. Today he send 2, but the first doesn't look as fun as the second, so I'll do that one later. Kory doesn't know of this blog, because I just found his. I've sent him on a quest to internet search me down. As his prize for finding it, I give you the solution to his second question:
Question:
Let's say (hypothetically) we are going out, and for your birthday I got you a pearl necklace... All well and good, untill you find out that it's fake, and I'm fake and in a heat of frustration you rip it off your neck.
One third of the "pearls" fell toward you, one sixth fell on the tear soaked pillows, one half of what remained (and one half of what remained thereafter and again one half of what remained thereafter) and so on, counting six times in all, fell everywhere else. 1161 "pearls" were found to remain unscattered. How many pearls were on the necklace when I gave it too you?
Hypothetically speaking of course.... I mean pearls, how 870's AD.
Answer:
Let x be the original number of pearls
If 1/3 scatter towards me, 2x/3 remain
If 1/6 fall on the pillow, (5/6)*(2x/3)=(5x/9) remain
solving for x,
x=2123
Am I right, Kory, or AM I RIGHT?
Sometimes Kory gives me really lame problems. This one was still pretty short but also really fun and cool and teary. Thanks KMath!
8 comments:
It seems to me that you made two incorrect statements in your solution.
1/6 - pillow
2/6 - scatter
3/6 - neither on pillow nor scatter
The remaining pearls are halved six times -> ((1/2)^7)x=1161...
Where x is the total number of pearls... x = 148608.
You considerd the pillow pearls from the remaining, and you have conducted some sort of intricate sum to calculate an exponent (that does not look like a Fourier Apprx)...
This problem could also be solved with only a sum of diminishing fractions (long).
As well, I apologize for the length of the questions, I prefer a quick logical answer then a long drawn out conclusion.... But if thats your taste, I can rock that way...
How's #1 comming?
K-o
No no! I love the short ones equally!
Okay so I interpreted the question to be that 1/3 fall towards me, and then 1/6 of those go to the pillow, its the remainder of those that are halved, halved, halved, halved, halved, halved.
Bummer! But if you interpret the question the same way as me- I then am right. But, now that I re-read it, yeah, I interpreted it wrong. Great now I have a wrong answer on my blog!
Why though did you put (1/2)^7? Why 7? Not 6?
awww how sweet... flirting through maths problems... :-)
to clarify, kory is one of my very best friend's boyfriend
you are a nerd and i love you
ahhh - okay. that explains the cheap fake pearls. Real love would be diamonds :-)
Ahhh... but of course...
It is .5^7 for the following reason:
you start with .5
which is then halved 6 times...
(.5)initial*(.5*.5*.5*.5*.5*.5)additional = .5^7
Sorry about the unclarity. I stil to not understand the SUM you used... why not a Pi (MULTIPLICATION) function?
As well,
How is the other problem going?
k
Wouldn't the answer, being that the question asks how many PEARLS were on the necklace when he gave it to you, be none?
Because they weren't pearls.
Post a Comment