# Posts Tagged ‘ Le Monde ’

## Le Monde puzzle [#5]

February 10, 2011
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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

## Le Monde puzzle [#4]

February 4, 2011
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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

## 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

## Le Monde puzzle [1]

January 10, 2011
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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

## 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

## Le Monde puzzle [49]

December 7, 2010
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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

## 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

## Le Monde puzzle [48]

December 1, 2010
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$Le Monde puzzle [48]$

This week(end), the Le Monde puzzle can be (re)written as follows (even though it is presented as a graph problem): Given a square 327×327 symmetric matrix A, where each non-diagonal entry is in {1,2,3,4,5} and , does there exist a triplet (i,j,k) such that Solving this problem in R is very easy. We can create

## Random graphs with fixed numbers of neighbours

November 24, 2010
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In connection with Le Monde puzzle #46, I eventually managed to write an R program that generates graphs with a given number n of nodes and a given number k of edges leaving each of those nodes. (My early attempt was simply too myopic to achieve any level of success when n was larger than

## Le Monde puzzle [43]

November 7, 2010
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Here is the puzzle in Le Monde I missed last week: Given a country with 6 airports and a local company with three destinations from each of the six airports, is it possible to find a circular trip with three intermediate stops from one of the airports? From all of the airports? One more airport