Tobee iz gowin awn a trip tah da Zen Masters' summit meeting. He kneadz tah leave foah hiz flight at 4:00 AM. He haz hiz suitcase awl packed. He kneadz tah getz hiz cloze in da dark zo he doesn't wake Amee & Myke upe. He haz hiz cloze awl laid owd, eggzept foah hiz sox. Hiz sox r nutt put into pairs yetz. He haz 18 white sox, and 16 black sox. Ow many sox wiyill he need tah grab in da dark tah make zur he haz two matching pairs (can be 4 black, 4 white, or 2 black + 2 white)?
13 comments:
Darn! I don't think the BuBe method is going to work on this one.
11
First I got 5 but something made me feel this was too easy so I might be doing something wrong. Then I realized what was going on. 5 would work for huminds. The Zen Mastah is not a humind.
What if Millie the Millipede had an unlimited supply of white and black socks and wanted to join the Zen Mastah. How many would she need to pull out to guarantee two pair?
And if you REALLY want to go for the BIG TIME, what's a general formula for the number of socks you'd need to pick if you were a creature with F feet.
Huminds have F=2
Zen Mastahs have F=4
Millipedes have F=1000
I think 11 would be the answer if you want a set of 4 matching socks ($ black or 4 white). If you want either four that match, or 2 white 2 black, 5 works I think. Here is why:
There can be only 3 combination of 4 socks, BBBW, WWWB, or WWBB. If you add an additional sock of either color to any of those combination, you can have either 4B, 4W, or 2W2B.
I am not 100% sure about this, because I adapted this puzzle from a humind with 2 feet to a cat with 4 feet. So if you can tell me why 5 doesn't work, I will settle for that, since you are the math mastah, TcT
My original 5 answer may have been "correct" after all but the whole thing hinges on what one means when one says a "pair" of socks for a cat. Huminds need 2 socks to make a "pair." I was thinking that a "pair" of socks for a cat should probably mean 4 socks. This interpretation makes your problem much more interesting and more difficult. It might not have been what you meant but let's say this is what is meant and see if we can solve it.
After pulling 6 socks out of the drawer, the "worst" situation would be something like
BWBWBW
i.e. no "pairs" yet. But the 7th sock is guaranteed to give the Mastah a "pair," either white or black.
Say he pulls a black, giving him a black "pair."
Then, the next "worst" thing would be pulling three more blacks cuz he would still be short that elusive second "pair" of socks.
So, the 10 socks he now has need to get one more sock. If it's a black, he'll have two black "pairs." It it's a white, it will match up with original 3 whites that were 1 short of a white "pair."
So, this is why you need to pull 11 to guarantee you get 2 "pair."
I think the problem was even more interesting than you intended. Or maybe I'm making all this up because I'm only humind and make miztakes.
Actually, we are both right! By 2 pairs, I meant 4 socks. But you thought I meant 8 socks. So for the 4 sock problem, I am right, and for the 8 sock problem, you are right. Sorry for the confusion!
hmmmm, see I was thinking there was 5 possible 4 sock combos, in addition to your BBBW, WWWB, or WWBB, I thought also BBBB and WWWW. Then I started to get confused and decided Tobee should wear sandles - they just seem so much more "zen"
sandels?
Whenever I can't spell something, I just type into Google. I typed "sandels" in and got:
Did you mean: sandals?
You are entirely right Miss BuBe, there is always BBBB and WWWW! But you still have to grab 5 in the dark just to be sure.
PS: Tobee said he will take the sandals option into serious consideration. But only in the summah.
Further insight into the problem of picking sox out of a drawer
A little something for everybody
http://primepuzzle.com/blog/feet.html
Enjoy!
TcT
Feedback encouraged
Loved it! Stripey socks and all - this must have netted you a few new words in TobeeSpeek
after re-reading the entire blog feet posting I am sticking with "Innovation knows when to let up".
This story of sox (and of how many times The Zen Mastah would need to reach into his drawer in the dark to get a "pair" of 4 for his trip) was interesting to finally take a look at. I'm a little slow to digest it all I am afraid, but it was fun to read everyone's comments. Wow! The links were interesting to look at too!
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