Another of those “drop-a-digit” Le Monde mathematical puzzle: Find all integers n with 3 or 4 digits, no exterior zero digit, and a single interior zero digit, such that removing that zero digit produces a divider of x. As in puzzle #904, I made use of the digin R function: and simply checked all integers […]
A recursive programming Le Monde mathematical puzzle: Given n tokens with 10≤n≤25, Alice and Bob play the following game: the first player draws an integer1≤m≤6 at random. This player can then take 1≤r≤min(2m,n) tokens. The next player is then free to take 1≤s≤min(2r,n-r) tokens. The player taking the last tokens is the winner. There is […]
About this #904 arithmetics Le Monde mathematical puzzle: Find all plural integers, namely positive integers such that (a) none of their digits is zero and (b) removing their leftmost digit produces a dividing plural integer (with the convention that one digit integers are all plural). a slight modification in the R code allows for a […]
Here are the most popular entries for 2014: 17 equations that changed the World (#2) 995 Le Monde puzzle [website] 992 “simply start over and build something better” 991 accelerating MCMC via parallel predictive prefetching 990 Bayesian p-values 960 posterior predictive p-values 849 Bayesian Data Analysis [BDA3] 846 Bayesian programming [book review] 834 Feller’s shoes […]
And yet another resolution of this combinatorics Le Monde mathematical puzzle: that puzzle puzzled many more people than usual! This solution is by Marco F, using a travelling salesman representation and existing TSP software. N is a golden number if the sequence {1,2,…,N} can be reordered so that the sum of any consecutive pair is a […]
As mentioned in the previous post, an alternative consists in finding the permutation of {1,…,N} by “adding” squares left and right until the permutation is complete or no solution is available. While this sounds like the dual of the initial solution, it brings a considerable improvement in computing time, as shown below. I thus redefined […]
A simple combinatorics Le Monde mathematical puzzle: N is a golden number if the sequence {1,2,…,N} can be reordered so that the sum of any consecutive pair is a perfect square. What are the golden numbers between 1 and 25? Indeed, from an R programming point of view, all I have to do is to […]
I learned something in R today thanks to Le Monde mathematical puzzle: A two-player game consists in A picking a number n between 1 and 10 and B and A successively choosing and applying one of three transforms to the current value of n n=n+1, n=3n, n=4n, starting with B, until n is larger than […]
A Le Monde mathematical puzzle in combinatorics: Given a permutation σ of {1,…,5}, if σ(1)=n, the n first values of σ are inverted. If the process is iterated until σ(1)=1, does this always happen and if so what is the maximal number of iterations? Solve the same question for the set {1,…,2014}. I ran the following basic R […]
A Le Monde mathematical puzzle once again in a Sudoku mode: In an nxn table, all integers between 1 and n appear n times. If max denotes the maximum over the numbers of different integers on all rows and columns, what is the minimum value of max when n=7? when n=11? I tried to solve […]
