Publications by xi'an
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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Le Monde puzzle [#1076]
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 identical slices and turn one slice upside down. If the only possibly moves are to ...
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Le Monde puzzle [#1081]
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 sure of the other’s number. What is the maximum numbe...
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more concentration, everywhere
Although it may sound like an excessive notion of optimality, one can hope at obtaining an estimator δ of a unidimensional parameter θ that is always closer to θ that any other parameter. In distribution if not almost surely, meaning the cdf of (δ-θ) is steeper than for other estimators enjoying the same cdf at zero (for instance ½ to make ...
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missing digit in a 114 digit number [a Riddler’s riddle]
A puzzling riddle from The Riddler (as Le Monde had a painful geometry riddle this week): this number with 114 digits 530,131,801,762,787,739,802,889,792,754,109,70?,139,358,547,710,066,257,652,050,346,294,484,433,323,974,747,960,297,803,292,989,236,183,040,000,000,000 is missing one digit and is a product of some of the integers between 2 and 99...
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Le Monde puzzle [#1083]
A Le Monde mathematical puzzle that seems hard to solve without the backup of a computer (and just simple enough to code on a flight to Montpellier): Given the number N=2,019, find a decomposition of N as a sum of non-trivial powers of integers such that (a) the number of integers in the sum is maximal or (b) all powers are equal to 4. Is it p...
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Le Monde puzzle [#1085]
A new Le Monde mathematical puzzle in the digit category: Given 13 arbitrary relative integers chosen by Bo, Abigail can select any subset of them to be drifted by plus or minus one by Bo, repeatedly until Abigail reaches the largest possible number N of multiples of 5. What is the minimal possible value of N under the assumption that Bo tries t...
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simulation fodder for future exams
Here are two nice exercises for a future simulation exam, seen and solved on X validated.The first one is about simulating a Gibbs sampler associated with the joint target exp{-|x|-|y|-a(y-x|} defined over IR² for a≥0 (or possibly a>-1). The conditionals are identical and non-standard, but a simple bound on the conditional density is the corre...
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