Publications by xi'an
Le Monde puzzle [#1111]
Another low-key arithmetic problem as Le Monde current mathematical puzzle: Notice that there are 10 numbers less than, and prime with 11, 100 less than and prime with 101, 1000 less than, and prime with 1111? What is the smallest integer N such that the cardinal of the set of M As it is indeed a case for brute force resolution as in the follow...
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poor statistics
I came over the weekend across this graph and the associated news that the county of Saint-Nazaire, on the southern border of Brittany, had a significantly higher rate of cancers than the Loire countries. The complete study written by Solenne Delacour, Anne Cowppli-Bony, amd Florence Molinié, is quite cautious about the reasons for this higher r...
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Le Monde puzzle [#1112]
Another low-key arithmetic problem as Le Monde current mathematical puzzle: Find the 16 integers x¹,x²,x³,x⁴,y¹,y²,y³,y⁴,z¹,z²,z³,z⁴,w¹,w²,w³,w⁴ such that the groups x¹,y¹,z¹,w¹, &tc., are made of distinct positive integers, the sum of the x’s is 24, of the y’s 20, of the z’s 19 and of the w’s 17. Furthermore, x¹...
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Le Monde puzzle [#1114]
Another very low-key arithmetic problem as Le Monde current mathematical puzzle: 32761 is 181² and the difference of two cubes, which ones? And 181=9²+10², the sum of two consecutive integers. Is this a general rule, i.e. the root z of a perfect square that is the difference of two cubes is always the sum of two consecutive integers squared? ...
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three birthdays and a numeral
The riddle of the week on The Riddler was to find the size n of an audience for at least a 50% chance of observing at least one triplet of people sharing a birthday, as is the case in the present U.S. Senate. The question is much harder to solve than for a pair of people but the formula exists!, as detailed on this blog entry, this X validated en...
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Le Monde puzzle [#1115]
A two-person game as Le weekly Monde current mathematical puzzle: Two players Amaruq and Atiqtalik are in a game with n tokens where Amaruq chooses a number 1 The run of a brute force R code like B=rep(-1,200);B[1:9]=1 for (i in 10:200){ v=matrix(-2,9,9) for (b in 2:9){ for (a in (2:9)[-b+1]) for (d in c(1,a,b)){ ...
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Galton’s board all askew
Since Galton’s quincunx has fascinated me since the (early) days when I saw a model of it as a teenager in an industry museum near Birmingham, I jumped on the challenge to build an uneven nail version where the probabilities to end up in one of the boxes were not the Binomial ones. For instance, producing a uniform distribution with the maxim...
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BayesComp 20 [schedule]
The schedule for the program is now available on the conference webpage of BayesComp 20, for the days of 7-10 Jan 2020. There are twelve invited sessions, including one j-ISBA session, and a further thirteen contributed sessions were selected by the scientific committee. And three tutorials on the first day. Looking forward seeing you in Florida!...
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Froebenius coin problem
A challenge from The Riddler last weekend came out as the classical Frobenius coin problem, namely to find the largest amount that cannot be obtained using only n coins of specified coprime denominations (i.e., with gcd equal to one). There is always such a largest value. For the units a=19 and b=538, I ran a basic R code that returned 9665 as th...
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riddle by attrition
The weekend riddle from The Riddler is rather straightforward [my wording and simplification]: Construct a decimal number X between 0 and 1 by drawing the first digit a¹ uniformly over {0,1,…,9}, the second digit a² uniformly over {0,1,…,9}, &tc., until 0 is attained. What is the expectation of this random variable X? Since each new digit h...
941 sym R (110 sym/1 pcs) 2 img