Monday Math Madness with Blinkdagger
17 Mar 2008 Quan Quach 27 comments 500 views
Introduction
Daniel and I are proud to present the first Monday Math Madness here at blinkdagger!!! Two weeks ago, Sol hosted a great math contest over at wildaboutmath.com, and this week, it is our turn. We hope you find the problem to be interesting as well as challenging. The prize for this week will consist of a 10 dollar gift certificate to Amazon. Take a look at the problem statement below, and remember to read the rules as well! Also, it would be great if anyone who reads this can spread the word either through word of mouth or by mentioning it on their blog. Thanks!
The Contest Problem
There are 1000 engineering-centric Leprechauns, all of whom are members of the prestigious group, Mensa. Each of the Leprechauns have an extremely high IQ (top 2% among the general population) and each Leprechaun is fully aware that all the other Leprechauns are also members of Mensa.
One day, the Leprechauns receive news that there is an abnormally large pot of gold at the end of the rainbow near China. All of the Leprechauns rush to the end of the rainbow and arrive simultaneously. In this situation, according to Leprechaun Lore, the treasure is to be divided by the following manner:
Every day, the Leprechauns will vote to either
1) send the youngest Leprechaun back to Ireland, or
2) split the pot of gold up among the remaining Leprechauns.
If 50% or more of the Leprechauns vote to split the pot of gold, the treasure gets split among the remaining Leprechauns. Otherwise, the youngest Leprechaun is sent back to Ireland. Assume that each Leprechaun know the ages of all Leprechauns. The process is repeated until the gold is split.
The question is: When will the gold be split?
The Rules
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Email your answers to mondaymathmadness at gmail dot com.
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Only one entry per person
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Answer must be explained. You must show your work! We will be the final judge on whether an answer was properly explained or not.
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The deadline to submit answers is March 25th 2008, Tuesday 12:00 AM Pacific Standard Time
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The winner will be chosen randomly from all the submittals using a random number generator.
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The winner will be announced at 9:00 AM PST March 28th, 2008.
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The winner will receive a 10 dollar gift certificate to Amazon.com!
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Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
27 Responses to “Monday Math Madness with Blinkdagger”
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Can I assume that every Leprechaun know about the age of all other Leprechauns ?
Yes, this can be assumed. Problem statement is modified to reflect this change.
I think you should also mention that the Leprechauns are greedy and want to get as much gold as possible
Yes, Leprechauns innately love pots of gold and will do almost anything to get more.
what is the upper and lower bounds of Lesprechauns age? Can it be taken as 4 and 94 as given in Mensa website?
I take it that “split the gold” means to share it equally?
Also, I’m assuming that despite their Mensa membership, these Leprechauns are rational and intelligent (and acting so as to maximize their own gold, without consideration of how much gold any particular other Leprechauns might get).
Harsha: I think the ages are to the nearest minute or day or something, not rounded to the nearest year, so the range doesn’t really matter.
Harsha:
Yes, the upper bound is 94 years old. The lower bound is 4 years old.
Joshua:
Yes, you are correct in your assumption.
Even in the top 2%, there is another 100% worth of variation. Do we assume that all leprechauns have equal intelligence and that all leprechauns are aware of this fact, or would some necessarily be (or think themselves to be) smarter than others?
Just to clarify: even though the ages are bound between 4 and 94, that doesn’t mean that there are only 91 distinct ages of Leprechaun, right? They can still be force ranked / sorted into a determined age-order from 1 to 1000. Let me know, otherwise this is an ENTIRELY different problem than what I first thought.
Rob,
That is correct. Assume that you can order the Leprechauns from oldest to youngest on a continuous curve. Thus, no two Leprechauns will share the same exact age. Another way of thinking about it is ranking the Leprechauns from 1 to 1000, in order of their age.
[...] Older students may enjoy this leprechaun logic puzzle: Monday Math Madness with Blinkdagger [...]
Hey, this is cool.
Might take the time to answer it if I have time (Exams are coming, I have to focus!) Will you post the answer with the explanation here after you pick a winner?
[...] To the Math geeks out there, check out this contest. Get the chance to win a $10 Amazon Gift Certificate by answering the problem. The deadline to [...]
Yup we will post solution on Monday, declare winner, and display honorable mentions!
Is this a math problem or a logic problem?
awww i dun like math nerds
Will the winner will be chosen randomly from all the submittals even if their answer is wrong?
Sam2k: when it comes to puzzles/riddles not out of textbook, math and logic goes hand in hand… this one with more emphasis on logic
FM2: Winner will be chosen from a pool of correct submissions
[...] Hey Everyone, today is the last day for you to submit answers to last week’s math contest, which you can find here. [...]
Can the youngest leprechauns have a few leprechaun babies, real quick?
So what’s the answer ?
The answer was announced in this post:
http://www.blinkdagger.com/blog/and-the-winner-is-joshua-zucker
I am working on a different problem. What would the answer be for a different number starting at 777 or 333?
I think Mike is a Geocacher in maine and is looking for the same answer I am….maybe?
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[...] None of these puzzles belong to me. And this is the only one that I know who to extend credit to. The rest, I think they’ve just sort of existed, forever. This one was a contest problem, posted by Quan Quach at Blinkdagger, as the second ever Monday Math Madness prize puzzle. Look here. [...]
[...] None of these puzzles belong to me. And this is the only one that I know who to extend credit to. The rest, I think they’ve just sort of existed, forever. This one was a contest problem, posted by Quan Quach at Blinkdagger, as the second ever Monday Math Madness prize puzzle. Look here. [...]