Monday Math Madness #16: Winner!
10 Oct 2008 Quan Quach 5 comments 49 views
MMM #16 Winner
The winner for this edition of MMM is Doug Hull from The MathWorks! Congratulations Doug. Doug just started a new blog so if you have ANY interest in MATLAB, you should scurry on over and immerse yourself in MATLAB goodness.
There was some slight confusion regarding the problem, and I will be the first to admit that it could have been presented more clearly. You can be sure that MMM #18 will be crystal clear! Hope everyone enjoyed the problem. Get ready for MMM #17, which will be hosted over at wildaboutmath.com on Monday!
Even though Doug is the winner, I have chosen to use a different reponse since Doug’s explanation was a tad lacking, but sufficient enough to win the prize.
The Answer by Nathan Picardat
If I understand your question correctly, it should take ten people to deduce which Yoshi is problematic, though it will take quite a bit of effort.
To begin with, each of nine people is given a subset of Yoshis comprising roughly half of the total Yoshis. The first person is given the first half; the second person is given the first and third quarters, the third person is given the first, third, fifth, and seventh eights, and so forth, until all ten people have been assigned Yoshis.
After the mass sitting has commenced, and a day has passed, half of them should be sore. Each will give testimony as to whether their set of half the Yoshis gave them pain, with each testimony halving the size of the set which may contain the potentially troublesome Yoshi, narrowing it thusly: A: 325, B: 162 or 163, C: 81 or 82, D: 40 or 41, E: 20 or 21, F: 10 or 11, G: 5 or 6, H: 2 or 3, I: 1 or 2, J: Only 1.
This will pinpoint the sore yoshi, but Mario will have caused a net five weeks of pain to his friends, and forced more than three-thousand collective yoshi-sittings. If he was truly the nice guy you make him out to be, Mario should’ve just called upon his 650 friends and have them each do one sitting, reducing the collective strain on both his friends and the Yoshis.
Also, it is my opinion that Mario should limit his friends to those capable of riding Yoshis and feeling the pain. Samus’ armor might protect her, as would Kirby’s status as being nothing more than a giant pink marshmallow. Stick with the Toadstools for best results; it’ll make them feel useful.
Other tactics that might be considered would be alternative forms of transportation, such as his yellow cape, a go-kart, or taking the warp-star just past the hidden water stage of Donut Plains (which Yoshi is pretty useless in, anyway).
Failing all that, he should just ask the Yoshis which one was giving him the riding pains. If they refuse to talk, Mario should just grab his brother (whom, I might add, is just as capable a warrior as Mario) and they could each ride a different Yoshi, gaurenteeing that at least one of them will be in their best fighting-form by the time they reach Bowser’s castle. Or better still, Mario could just give up on determining which Yoshi is problematic, and just use a single friend sitting on a single Yoshi, to find a single Yoshi that isn’t problematic, and use that Yoshi exclusivly.
Shout Outs!
The following people correctly answered the question:
Doug Hull
Nathan Picardat
Efrit Freeq
Joseph A. Schreier
C. de Jong
Marijn Jongerden
Richard Berlin for his interesting answer (although technically it doesn’t really answer the question asked. But it DOES allow Mario to with 100% certainty make it to Bowser’s Castle of Doom).
Richard’s Answer:
Only one friend is needed.
There is an implication that the problematic Yoshi has to be found in one day, but this is not true. Mario has to have a safe Yoshi to ride one day hence, but that is a simpler problem that can be solved first.
Mario calls up Luigi; together they number the Yoshis, and Luigi rides #1. The next day, if Luigi is sore, the problematic Yoshi has been found and Mario rides another one. Otherwise, Mario rides away on #1, and Luigi rides #2, #3, #4 on successive days until he finds the one who causes soreness. To speed things up, when Mario comes back from his battle with Bowser (victorious, of course!) he can then afford to help Luigi test Yoshis.
5 Responses to “Monday Math Madness #16: Winner!”
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About Nathan’s answer:
“After the mass sitting has commenced, and a day has passed, half of them should be sore.”
Since the testers are given the first half, first quarter, first eighth and so on of the 650…
If the problematic yoshi was in fact the first one tested, wouldn’t all of them feel sore?
“If the problematic yoshi was in fact the first one tested, wouldn’t all of them feel sore?”
You’re completely correct on that. What I should have said is something along the lines of “/on average/, half of them should be sore.” After all, if the problematic Yoshi was the last one, none of them would be sore.
I see absolutely no problem with Richard’s answer, in fact it’s the answer that I cam up with myself, however I only saw the problem after the contest was over. Just because it does not answer the question in the way you meant for it to be answered does not make it wrong. The problem given set a time limit as to how long Mario could be involved, but set no limit to how long it might take to actually find the problematic Yoshi.
Here’s a link to the original problem: http://www.blinkdagger.com/monday-math-madness/mmm-15-mario-and-the-problematic-yoshi
The question states that:
What is the minimum number of friends that Mario will have to call upon to determine with 100% certainty which Yoshi is the Problematic Yoshi?
Thus, 1 is not the answer. The whole point of the contest is to answer the question that is posed. Innovation is good, but it still has to address the original problem statement. And the time limit is one day as that is the time Mario has before the showdown with Bowser.
Hope to see you at the next iteration of MMM!
Quan
3 friends is the minimum.