mathematical puzzle

R midterms

November 9, 2012 | xi'an

Here are my R midterm exams, version A and version B in English (as students are sitting next to one another in the computer rooms), on simulation methods for my undergrad exploratory statistics course. Nothing particularly exciting or innovative! Dedicated ‘Og‘s readers may spot a few Le Monde puzzles ... [Read more...]

the large half now

October 28, 2012 | xi'an

The little half puzzle proposed a “dumb’ solution in that players play a minimax strategy. There are 34 starting values less than 100 guaranteeing a sure win to dumb players. If instead the players maximise their choice at each step, the R code looks like this: and there are now 66 (=100-34, indeed!) ... [Read more...]

the little half (another Le Monde puzzle)

October 27, 2012 | xi'an

I found this Le Monde puzzle of June 16 I had stored and then somehow forgotten with my trips to Japan and Australia: There are n beans in a box, with 98≤n≤102). Two players take at each round either one bean from the box or “the little half” (i.e. the ... [Read more...]

Le Monde puzzle (rainy Sunday!)

October 20, 2012 | xi'an

On October 14, the weekend edition of Le Monde had the following puzzle: consider four boxes that contain all integers between 1 and 9999, in such a way that for any N, N, 2N, 3N, and 4N are in four different boxes. If 1,2,3 and 4 are in boxes labelled 1,2,3 and 4, respectively, in [...] [Read more...]

Le Monde puzzle [#783]

July 20, 2012 | xi'an

In a political party, there are as many cells as there are members and each member belongs to at least one cell. Each cell has five members and an arbitrary pair of cells only shares one member. How many members are there in this political party? Back to the mathematical ... [Read more...]

\verbatim [beamer package]

June 11, 2012 | xi'an

Once again working on my slides for the AMSI Lecture 2012 tour, it took me a while to get the following LaTeX code (about the family reunion puzzle) to work: \begin{frame}[fragile,label=notleM2] \slidetitle{A family meeting} \begin{block}{Random switch of couples} \only{ \begin{itemize} \item Pick two ... [Read more...]

Le Monde puzzle [#755?]

January 27, 2012 | xi'an

Le Monde puzzle of last weekend was about sudoku-like matrices. Consider an (n,n) matrix containing the integers from 1 to n². The matrix is “friendly” if the set of the sums of the rows is equal to the set of the sum of the columns. Find examples for n=4,5,6. Why ... [Read more...]

Le Monde puzzle [#754]

December 25, 2011 | xi'an

The pre-X’mas puzzle in Le Monde weekend edition is about “magical numbers” having as digits all digits between 0 and n (at least once) and being multiple of all digits between 1 and (n+1). Easy, isn’t it?! I thought so while driving down to the Alps on Saturday and (on ... [Read more...]

Le Monde puzzle [#752]

December 8, 2011 | xi'an

After a loooong break, here is one Le Monde mathematical puzzle I had time to look at, prior to going to Dauphine for a Saturday morning class (in replacement of my R class this week)! The question is as follows: A set of numbers {1,…,N} is such that multiples of 4 ... [Read more...]

le Monde puzzle [#745]

October 20, 2011 | xi'an

The puzzle in Le Monde this weekend is not that clear (for a change!), so I may be confused in the following exposition: Three card players are betting with a certain (and different) number of chips each, between 4 and 9. After each game, the looser doubles the number of chips of ... [Read more...]

Le Monde puzzle [#739]

September 9, 2011 | xi'an

The weekend puzzle in Le Monde this week is again about a clock.  Now, the clock has one hand and x ticks where a lamp is either on or off. The hand moves from tick to tick and each time the lights go on or off depending on whether or ... [Read more...]

Le Monde puzzle [#738]

September 1, 2011 | xi'an

The Friday puzzle in Le Monde this week is about “friendly perfect squares”, namely perfect squares x2__10 and y2__10 with the same number of digits and such that, when drifting all digits of x2 by the same value a (modulo 10), one recovers y2. For instance, 121 is “friend” with 676. Here is ... [Read more...]

Le Monde puzzle [#737 re-read]

August 27, 2011 | xi'an

As a coincidence, while I was waiting for the solution to puzzle #737 published this Friday in Le Monde, the delivery (wo)man forgot to include the weekend magazine and I had to buy it this morning with my baguette (as if anyone cares!). The solution is (y0,z0,w0)=(38,40,46) and…... [Read more...]

Le Monde puzzle [#737]

August 26, 2011 | xi'an

The puzzle in the weekend edition of Le Monde this week can be expressed as follows: Consider four integer sequences (xn), (yn), (zn), and (wn), such that and, if u=(xn,yn,zn,wn), for i=1,…,4, if ui is not the maximum of u and otherwise. Find the first return ... [Read more...]

Le Monde puzzle [#28]

July 22, 2011 | xi'an

The puzzle of last weekend in Le Monde was about finding the absolute rank of x9 when given the relative ranks of x1,….,x8 and the possibility to ask for relative ranks of three numbers at a time. In R terms, this means being able to use or yet being ... [Read more...]

Le Monde puzzle [#14.2]

May 14, 2011 | xi'an

I received at last my weekend edition of Le Monde and hence the solution proposed by the authors (Cohen and Busser) to the puzzle #14. They obtain a strategy that only requires at most 19 steps. The idea is to start with a first test, which gives a reference score S0, and ... [Read more...]

Le Monde puzzle [#14]

May 13, 2011 | xi'an

Last week Le Monde puzzle (I have not received this week issue yet!) was about deriving an optimal strategy in less than 25 steps for finding the 25 answers to a binary multiple choice test, when at each trial, only the number of correct answers is known. Hence, if the correct answers ... [Read more...]

Le Monde puzzle #13

April 13, 2011 | xi'an

This week, Le Monde offers not one but three related puzzles: Is it possible to label the twelve edges of a cube by consecutive numbers such that the sum of the edge numbers at any of the eight nodes is constant? Is it possible to label the eight nodes of ... [Read more...]

Le Monde puzzle [#8]

March 29, 2011 | xi'an

Another mathematical puzzle from Le Monde that relates to a broken calculator (skipping the useless tale): Given a pair of arbitrary positive integers (x,y) a calculator can either substract the same integer [lesser than min(x,y)] from both x and y or multiply either x or y by 2. ... [Read more...]
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