Posts Tagged ‘ mathematical puzzle ’

Le Monde puzzle [#7]

March 26, 2011
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Le Monde puzzle [#7]

The mathematical puzzle from the weekend edition of Le Monde from a few weeks ago was not too hard to solve by induction but my R code failed miserably! The puzzle was as follows: A calculator is broken in such a way that it starts by exhibiting 0, then pressing 4, 6 or 0 keeps

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One bicycle for two

March 22, 2011
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One bicycle for two

Robin showed me a mathematical puzzle today that reminded me of a story my grand-father used to tell. When he was young, he and his cousin were working in the same place and on Sundays they used to visit my great-grand-mother in another village. However, they only had one bicycle between them, so they would

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Le Monde puzzle [#6]

February 17, 2011
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Le Monde puzzle [#6]

A simple challenge in Le Monde this week: find the group of four primes such that any sum of three terms in the group is prime and the overall sum is minimised. Here is a quick exploration by simulation, using the schoolmath package (with its imperfections): A=primes(start=1,end=53) lengthA=length(A) res=4*53 for (t in 1:10^4){ B=sample(A,4,prob=1/(1:lengthA)) sto=is.prim(sum(B))

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Le Monde puzzle [#5]

February 10, 2011
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Le Monde puzzle [#5]

Another Sudoku-like puzzle from the weekend edition of Le Monde. The object it starts with is a 9×9 table where each entry is an integer and where neighbours take adjacent values. (Neighbours are defined as north, west, south and east of an entry.) The question is about whether or not it is possible to find

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Le Monde puzzle [#4]

February 4, 2011
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Le Monde puzzle [#4]

A fairly simple puzzle in this weekend Le Monde magazine: given five points on a line such that their pairwise distances are 1,2,4,…,14,18,20, find the respective positions of the five points over the line and deduce the missing distances. Without loss of generality, we can set the first point at 0 and the fifth point

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R exam

January 30, 2011
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R exam

I spent most of my Saturday perusing R codes to check the answers written by my students to the R exam I gave two weeks ago… The outcome is mostly poor, even though some managed to solve a fair part of the long problem. Except for the few hopeless cases who visibly never wrote a

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Le Monde puzzle [1]

January 10, 2011
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Le Monde puzzle [1]

Following the presentation of the first Le Monde puzzle of the year, I tried a simulated annealing solution on an early morning in my hotel room. Here is the R code, which is unfortunately too rudimentary and too slow to be able to tackle n=1000. #minimise \sum_{i=1}^I x_i #for 1\le x_i\le 2n+1, 1\e i\le I

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Le Monde puzzle [52|solution]

January 1, 2011
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Le Monde puzzle [52|solution]

I have now received the first issue of Le Monde magazine, including the solution to puzzle #52 I solved just in time by simulated annealing! The trick is in using the following theorem: Iter(1,x,y) is divisible by 10x-1 if and only if y is divisible by 10x-1. Then the value to be found is divisible

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Le Monde puzzle [49]

December 7, 2010
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Le Monde puzzle [49]

Here is a quick-and-dirty solution to Le Monde puzzle posted a few days ago: the R code counts the number of winning tickets between 1 and N, and stops when there is a proportion of 10% of winning tickets. #winning ticket win=function(n){ #decimal digits decomposition x=rep(0,4) x=n%%10 m=(n-x)/10 x=m%%10 m=(m-x)/10 x=m%%10 m=(m-x)/10 x=m%%10 tic=0 for

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Le Monde puzzle [48: resolution]

December 4, 2010
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Le Monde puzzle [48: resolution]

The solution to puzzle 48 given in Le Monde this weekend is rather direct (which makes me wonder why the solution for 6 colours is still unavailable..) Here is a quick version of the solution: Consider one column, 1 say. Since 326=5×65+1, there exists one value c with at least 66 equal to c. Among

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