Blog Archives

Le Monde puzzle [#959]

April 19, 2016
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Le Monde puzzle [#959]

Another of those arithmetic Le Monde mathematical puzzle: Find an integer A such that A is the sum of the squares of its four smallest dividers (including1) and an integer B such that B is the sum of the third poser of its four smallest factors. Are there such integers for higher powers? This begs

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Le Monde puzzle [#958]

April 10, 2016
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Le Monde puzzle [#958]

A knapsack Le Monde mathematical puzzle: Given n packages weighting each at most 5.8kg for a total weight of 300kg, is it always possible to allocate these packages  to 12 separate boxes weighting at most 30kg each? weighting at most 29kg each? This can be checked by brute force using the following R code and

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Statistical rethinking [book review]

April 5, 2016
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Statistical rethinking [book review]

Statistical Rethinking: A Bayesian Course with Examples in R and Stan is a new book by Richard McElreath that CRC Press sent me for review in CHANCE. While the book was already discussed on Andrew’s blog three months ago, and enthusiastically recommended by Rasmus Bååth on Amazon, here are the reasons why I

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Le Monde puzzle [#956]

April 4, 2016
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Le Monde puzzle [#956]

A Le Monde mathematical puzzle with little need of R programming: Does there exist a function f from N to N such that (i) f is (strictly) increasing, (ii) f(n)≥n, and (iii) f²(n)=f(f(n))=3n? Indeed, the constraints imply (i) f²(0)=0, hence that that f(0)=0, (ii) f(1)=2 as it can be neither 1 (else f²(1) would be equal

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another riddle

March 28, 2016
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another riddle

A very nice puzzle on The Riddler last week that kept me busy on train and plane rides, runs and even in between over the weekend. The core of the puzzle is about finding the optimal procedure to select k guesses about the value of a uniformly random integer x in {a,a+1,…,b}, given that each

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Le Monde puzzle [#954]

March 24, 2016
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Le Monde puzzle [#954]

A square Le Monde mathematical puzzle: Given a triplet (a,b,c) of integers, with a<b<c, it satisfies the S property when a+b, a+c, b+c, a+b+c are perfect squares such that a+c, b+c, and a+b+c are consecutive squares. For a given a, is it always possible to find a pair (b,c) such (a,b,c) satisfies S? Can you

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Le Monde puzzle [#952]

March 18, 2016
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Le Monde puzzle [#952]

A quite simple Le Monde mathematical puzzle again with Alice and Bob: In a multiple choice questionnaire with 50 questions, Alice gets a score s such that Bob can guess how many correct (+5 points), incorrect (-1 point) and missing (0 point) Alice got when adding that Alice could not have gotten s-2 or s+2.

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preserving frequencies without resampling

March 8, 2016
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preserving frequencies without resampling

An interesting question came up on X validated a few days ago: given a probability vector p=(p¹,…,p⁷), is there a way to pick 5 values in {1,…,7} without replacement and still preserve the probability repartition in the resulting sample? In other words, is there a sampling without replacement strategy that leads to for i=1,…,7..? Unless

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Amazonish warning

March 1, 2016
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Amazonish warning

As in previous years, I want to repost a warning to ‘Og readers that all http links to Amazon.com products found on this ‘Og are actually susceptible to reward me with an advertising percentage if a purchase is made by the reader in the 24 hours following the entry

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twilight zone [of statistics]

February 25, 2016
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twilight zone [of statistics]

“I have decided that mixtures, like tequila, are inherently evil and should be avoided at all costs.” L. Wasserman Larry Wasserman once remarked that finite mixtures were like the twilight zone of statistics, thanks to the numerous idiosyncrasies associated with such models. And George Casella had similar strong reservations about mixture estimation. Avi Feller and

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