mathematical puzzle

Le Monde puzzle [#7]

March 26, 2011 | xi'an

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 ... [Read more...]

One bicycle for two

March 22, 2011 | xi'an

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 ... [Read more...]

Le Monde puzzle [#6]

February 17, 2011 | xi'an

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)[... [Read more...]

Le Monde puzzle [#5]

February 10, 2011 | xi'an

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 ... [Read more...]

Le Monde puzzle [#4]

February 4, 2011 | xi'an

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 ... [Read more...]

R exam

January 30, 2011 | xi'an

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 ... [Read more...]

Le Monde puzzle [1]

January 10, 2011 | xi'an

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_... [Read more...]

Le Monde puzzle [52|solution]

January 1, 2011 | xi'an

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 ... [Read more...]

Le Monde puzzle [49]

December 7, 2010 | xi'an

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[4]=n%%10 m=(... [Read more...]

Le Monde puzzle [48: resolution]

December 4, 2010 | xi'an

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 [...] [Read more...]

Le Monde puzzle [48]

December 1, 2010 | xi'an

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 ... [Read more...]

Le Monde puzzle [43]

November 7, 2010 | xi'an

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 ... [Read more...]

Le Monde puzzle [42]

October 24, 2010 | xi'an

An interesting suduko-like puzzle for this week puzzle in Le Monde thi A 10×10 grid is filled by a random permutation of {0,…,99}. The 4 largest figures in each row are coloured in yellow and the 4 largest values in each column are coloured in red. What is the range of the number of ... [Read more...]

Le Monde puzzle [41]

October 17, 2010 | xi'an

The current puzzle in Le Monde this week is again about prime numbers: The control key on a credit card is an integer η(a) associated with the card number a such that, if the card number is c=ab, its key η(c) satisfies η(c)=η(a)+η(b)-1. There is only ... [Read more...]

Le Monde puzzle [40]

October 10, 2010 | xi'an

The puzzle in Le Monde this week[end] is called the “square five” (sic!): Two players each have twenty-five cards with five times each of the digits 1,2,3,4,5. They alternate putting one card on top of the pile, except that they can instead take an arbitrary number of consecutive cards from ... [Read more...]

Le Monde puzzle [34]

October 3, 2010 | xi'an

Since the puzzle in this week (-end) edition of Le Monde is not (easily) solvable via an R program, I chose to go back to an older puzzle that my students can solve. Eleven [distinguishable] token are [arbitrarily] distributed around a 200 meter perimeter-long ring. They all start moving at the ... [Read more...]

Le Monde puzzle [38]

September 29, 2010 | xi'an

Since I have resumed my R class, I will restart my resolution of Le Monde mathematical puzzles…as they make good exercises for the class. The puzzle this week is not that exciting: Find the four non-zero different digits a,b,c,d such that abcd is equal to the ... [Read more...]

Candy branching process

May 5, 2010 | xi'an

The mathematical puzzle in the latest weekend edition of Le Monde is as follows: Two kids are given three boxes of chocolates with a total of 32 pieces. Rather than sharing evenly, they play the following game: Each in turn, they pick one of the three boxes, empty its contents in ... [Read more...]

Solving the rectangle puzzle

March 15, 2010 | xi'an

Given the wrong solution provided in Le Monde and comments from readers, I went to look a bit further on the Web for generic solutions to the rectangle problem. The most satisfactory version I have found so far is Mendelsohn’s in Mathematics Magazine, which gives as the maximal number ... [Read more...]

Wrong puzzle of the week [w10]?!

March 12, 2010 | xi'an

In the weekend supplement to Le Monde, the solution of the rectangle puzzle is given as 32 black squares. I am thus… puzzled!, since my R program there provides a 34 square solution. Am I missing a hidden rectangle in the above?! Given that the solution in Le Monde is not based ... [Read more...]
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