Matheletics ‘13

9 responses to “Matheletics ‘13”

1. 

   jurvetson

   Mar 8, 2013 at 6:36 am

   Example questions from today’s test, with "small and large case" versions worth 10 and 20 points respectively…

   Hotel Transylvania: In her 118th birthday party, Mavis invites N friends to Hotel Transylvania. Count Dracula- Mavis’ father, orders a large rectangular cake. Before cutting the cake, all friends of Mavis started fighting in order to get the biggest piece of cake. So Jonathan, the only human in the party, used his master brain and gave a solution to resolve the fight. He suggested to cut the cake in exactly N equal pieces so that each friend of Mavis gets equal amount of cake. Each piece should be of the shape of the cuboid. To impress Mavis, Jonathan suggests to cut the cake in such a way that requires minimum number of cuts. Your task is to help Jonathan and find the minimum number of cuts required to divide the cake in exactly N equal pieces. Small Case: N = 13860 Large Case: N = 1010824870255200

   Strange Fractions: Any fraction in its lowest form can be represented as sum of reciprocals of Natural numbers. But this representation is not unique. Let two sets of reciprocals be (p1, p2, …, pn) and (q1, q2, …, qk). We say, the first is lexicographically lesser than the second if there is some m, 1 <= m <= min(n,k) such that,p1 = q1, p2 = q2, …, pm-1 = qm-1 and pm <= qm. Given a fraction in its lowest form, let it can be represented as a sum of reciprocals of the set (p1,p2,..,pk). For all such sets find the sum of the elements of the set which is lexicographically smallest. Small Case: a/b = 231/431 Large case: a/b = 1234/4321

   Permutation: For any positive integer n, determine the number of permutations (a1, a2, . . . , an) of the set {1, 2, . . . , n} with the following property: 2(a1 + a2 + . . .+ ak) is divisible by k for each k in [1, n], where [] denotes a closed interval.
   Answer should be number of permutations modulo 1000000007 i.e. (10^9 + 7). Small Case: 10000 (10^4) Large Case: 10^18

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2. 

   seatonsnet

   Mar 8, 2013 at 7:21 am

   [http://www.flickr.com/photos/jurvetson] Mulling it over, it would seem to me that the answer to the problem you mention is that Jonathan, being the only human in the group gets to eat the whole cake by himself as vampires can’t eat cake… something to do with blood sugar, I believe.

   Later, after he eats the cake, I imagine Mavis, her dad and the guests eat Jonathan as he is the only human being in the group and by now they all must be famished watching him work all this out in his head (vampires are notoriously stingy with office supplies) .

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3. 

   scleroplex

   Mar 8, 2013 at 10:48 am

   congratulations steve 🙂
   very special!!
   something to savour for the rest of his life.

   Reply
4. 

   heet_myser

   Mar 8, 2013 at 3:48 pm

   Pretty awesome! It’s wonderful when children are able to overcome their genetic deficiencies. 😉

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5. 

   jurvetson

   Mar 8, 2013 at 6:43 pm

   Thanks, and love the humor.

   The other parent wrote:
   "I did a little research and found out that the leader, Anton Lunyov, is also the leader on Project Euler. He’s a Ukranian PhD who does work for Facebook. The other guy "romka" appears to do work for Yandex, which is the leading Russian search engine."

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6. 

   seatonsnet

   Mar 8, 2013 at 7:24 pm

   [http://www.flickr.com/photos/jurvetson] Getting serious for a moment. If your boy is already batting in this league math-wise, I think he should start learning languages and get into philosophical problems of logic and even learn to draw, in order to explore other areas where this type of intelligence can broaden and develop. The danger is to become a one trick pony before his time,

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7. 

   Wolfram Burner

   Mar 9, 2013 at 3:29 am

   wow.

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8. 

   js.brain

   Mar 9, 2013 at 4:57 am

   Congratulations! what great news! We too we are blowing away by this.
   It is fascinating!

   Reply
9. 

   sbove

   Mar 11, 2013 at 3:28 am

   Wolfgang Amadeus Jurvetson.

   Reply