Publications by xi'an
Le Monde puzzle [#1068]
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=a²a³…. Find the largest refined integer x such the sequence of the succes...
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Le Monde puzzle [#1066]
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. For the inner table, this is straightforward as ...
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Le Monde puzzle [#1070]
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. How many steps from left to right? Painful ...
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ABC intro for Astrophysics
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!). As well as a longer coverage of Bayesian foundations and computations by Da...
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Le Monde puzzle [#1072]
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 both gold circles, respectively ...
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Le Monde puzzle [#1073]
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 a Gordia...
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Le Monde puzzle [#1075]
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 everywhere? Is this feasible for any configuration? ...
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Le Monde puzzle [#1078]
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 answer to the fourth question (iv) are all digits...
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Le Monde puzzle [#1075]
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 the usual integer2digits function!) le=solz=3 while ...
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running plot [and simulated annealing]
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 determining the most dispersed points in a unit disc. Related To leave a comment for the author, pl...
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