A “he said-she said” Le Monde mathematical puzzle (again in the spirit of the famous Singapore high-school birthdate problem): Abigail and Corentin are both given a positive integer, a and b, such that a+b is either 19 or 20. They are asked one after the other and repeatedly if they are ...

A cheezy Le Monde mathematical puzzle : (which took me much longer to find [in the sense of locating] than to solve, as Warwick U does not get a daily delivery of the newspaper [and this is pre-Brexit!]): Take a round pizza (or a wheel of Gruyère) cut into seven ...

Last weekend, I found out a way to run updated plots within a loop in R, when calling plot() within the loop was never updated in real time. The above suggestion of including a Sys.sleep(0.25) worked perfectly on a simulated annealing example for deter...

A new Le Monde mathematical puzzle in the digit category: Find the largest number such that each of its internal digits is strictly less than the average of its two neighbours. Same question when all digits differ. For instance, n=96433469 is such a number. When trying pure brute force (with ...

Recalling Le Monde mathematical puzzle  first competition problem Given yay/nay answers to the three following questions about the integer 13≤n≤1300 (i) is the integer n less than 500? (ii) is n a perfect square? (iii) is n a perfect cube?  n cannot be determined, but it is certain that any ...

A Le Monde mathematical puzzle from after the competition: A sequence of five integers can only be modified by subtracting an integer N from two neighbours of an entry and adding 2N to the entry.  Given the configuration below, what is the minimal number of steps to reach non-negative entries ...

And here is Le Monde mathematical puzzle  last competition problem Find the number of integers such that their 15 digits are all between 1,2,3,4, and the absolute difference between two consecutive digits is 1. Among these numbers how many have 1 as their three-before-last digit and how many have 2? Combinatorics!!! While it seems like […]

The penultimate Le Monde mathematical puzzle  competition problem is once again anti-climactic and not worth its points: For the figure below [not the original one!], describing two (blue) half-circles intersecting with a square of side 20cm, and a (orange) quarter of a circle with radius 20cm, find the radii of ...

Today I received in the mail a copy of the short book published by edp sciences after the courses we gave last year at the astrophysics summer school, in Autrans. Which contains a quick introduction to ABC extracted from my notes (which I still hope to turn into a book!). ...

Rewording Le Monde mathematical puzzle  fifth competition problem For the 3×3 tables below, what are the minimal number of steps to move from left to rights when the yellow tokens can only be move to an empty location surrounded by two other tokens? In the 4×4 table below, there are 6 green tokens. ...

A purely (?) algorithmic Le Monde mathematical puzzle For the table below, what is the minimal number of steps required to reach equal entries when each step consists in adding ones to three entries sitting in a L, such as (7,11,12) or (5,6,10)? Same question for the inner table of four in yellow. ...

And here is the third Le Monde mathematical puzzle  open for competition: Consider for this puzzle only integers with no zero digits. Among these an integer x=a¹a²a³… is refined if it is a multiple of its scion, the integer defined as x without the first digit, y=...

The second Le Monde mathematical puzzle in the new competition is sheer trigonometry: When in the above figures both triangles ABC are isosceles and the brown segments are all of length 25cm, find the angle in A and the value of DC², respectively. This could have been solved by R ...

Recalling Le Monde mathematical puzzle  first competition problem For the X table below, what are the minimal number of lights that are on (green) to reach the minimal and maximal possible numbers of entries (P) with an even (P as pair) number of neighbours with lights on? In the illustration ...

A second Riddle(r), with a puzzle related with the integer set Ð={,12,3,…,N}, in that it summarises as Given a random walk on Ð, starting at the middle N/2, with both end states being absorbing states, and a uniform random move left or right of the current value to the (integer) ...

A penultimate Le Monde mathematical puzzle  before the new competition starts [again!] For a game opposing 40 players over 12 questions, anyone answering correctly a question gets as reward the number of people who failed to answer. Alice is the single winner: what is her minimal score? In another round, Bob is ...

There will be a symposium on ABC in Montréal this coming December, the day before NIPS, in a continuation of past years NIPS workshops. While invited speakers and panelists have been selected by the committee, a call for papers is open. Note that in continuation with the best “ABC ...

I made the “capital” mistake of walking across the entire NUS campus this morning, which is quite green and pretty, but which almost enjoys an additional dimension brought by such an intense humidity that one feels having to get around this humidity!, a feature I have managed to completely erase ...

In the Riddler of August 18, two riddles connected with the integer set Ð={2,3,…,10}: Given a permutation of Ð, what is the probability that the most likely variation (up or down) occurs at each term? Given three players choosing three different integers in Ð sequentially, and rewards in Ð allocated to the closest of the […]

I came across this question on X validated that wondered about one of our examples in Monte Carlo Statistical Methods. We have included a section on Laplace approximations in the Monte Carlo integration chapter, with a bit of reluctance on my side as this type of integral approximation does not ...