Publications by xi'an
Le Monde puzzle [#1127]
A permutation challenge as Le weekly Monde current mathematical puzzle: When considering all games between 20 teams, of which 3 games have not yet been played, wins bring 3 points, losses 0 points, and draws 1 point (each). If the sum of all points over all teams and all games is 516, was is the largest possible number of teams with no draw in e...
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a very quick Riddle
A very quick Riddler’s riddle last week with the question Find the (integer) fraction with the smallest (integer) denominator strictly located between 1/2020 and 1/2019. and the brute force resolution for (t in (2020*2019):2021){ a=ceiling(t/2020) if (a*2019<t) sol=c(a,t)} leading to 2/4039 as the target. Note that Related To leave...
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MCMC, with common misunderstandings
As I was asked to write a chapter on MCMC methods for an incoming Handbook of Computational Statistics and Data Science, published by Wiley, rather than cautiously declining!, I decided to recycle the answers I wrote on X validated to what I considered to be the most characteristic misunderstandings about MCMC and other computing methods, using a...
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another easy Riddler
A quick riddle from the Riddler In a two-person game, Abigail and Zian both choose between a and z. Abigail win one point with probability .9 if they choose (a,a) and with probability 1 if they choose (a,z), and two points with probability .4 if they choose (z,z) and with probability .6 if they choose (z,a). Find the optimal probabilities δ and ...
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Le Monde puzzle [#1130]
A two-player game as Le weekly Monde current mathematical puzzle: Abishag and Caleb fill in alternance a row of N boxes in a row by picking one then two then three &tc. consecutive boxes. When a player is unable to find enough consecutive boxes, the player has lost. Who is winning when N=29? When N=30? Using a basic recursive search for the opt...
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Le Monde puzzle [#1129]
A number challenge as Le weekly Monde current mathematical puzzle: When the three consecutive numbers 110, 111 and 112, they all are multiples of the sum of their digits. Are there 4 consecutive numbers with three digits like this? A contrario, does there exist 17 consecutive numbers with three digits such that they cannot be divided by the sum ...
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SMC on the 2019-2020 nCoV outbreak
Two weeks ago, Kurcharski et al., from the CMMID nCoV working group at the London School of Hygiene and Tropical Medicine, published on medrXiv a statistical analysis via a stochastic SEIR model of the evolution of the 2019-2020 nCoV epidemics, with prediction of a peak outbreak by late February in Wuhan and a past outbreak abroad. Here are some ...
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Le Monde puzzle [#1132]
A vaguely arithmetic challenge as Le weekly Monde current mathematical puzzle: Given two boxes containing x and 2N+1-x balls respectively. If one proceeds by repeatedly transferring half the balls from the even box to the odd box, what is the largest value of N for which the resulting sequence in one of the boxes covers all integers from 1 to 2N...
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multiplying the bars
The latest Riddler makes the remark that the expression |-1|-2|-3| has no unique meaning (and hence value) since it could be | -1x|-2|-3 | = 5 or |-1| – 2x|-3| = -5 depending on the position of the multiplication sign and asks for all the possible values of |-1|-2|…|-9| which can be explored by a recursive R function for computing |-i...
1082 sym R (557 sym/2 pcs)
chain of lynx and drove of hares
A paper (and an introduction to the paper) in Nature this week seems to have made progress on the existence of indefinite predator-prey cyles. As in the lynx/hare dataset available on R. The paper is focusing on another pair, an invertebrate and its prey, an algae. For which the authors managed a 50 cycle sequence. What I do not get about this ex...
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