R midterms

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 … Continue reading

the large half now

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: solveO=function(n){ if … Continue reading

Le Monde puzzle (rainy Sunday!)

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 which box is 972 … Continue reading

Le Monde puzzle [#783]

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 puzzles of Le Monde … Continue reading

\verbatim [beamer package]

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 … Continue reading

Le Monde puzzle [#755?]

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 is there no friendly … Continue reading

Le Monde puzzle [#754]

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 … Continue reading

Le Monde puzzle [#752]

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 are tagged C and multiples … Continue reading

le Monde puzzle [#745]

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 the winner (while … Continue reading

Le Monde puzzle [#739]

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 not both  neighbours were in the same state the previous time. … Continue reading

Le Monde puzzle [#738]

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 … Continue reading

Le Monde puzzle [#737 re-read]

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…it does not … Continue reading

Le Monde puzzle [#737]

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 time n (if any) such that … Continue reading