A game-related Le Monde mathematical puzzle: Starting with a pile of 10⁴ tokens, Bob plays the following game: at each round, he picks one of the existing piles with at least 3 tokens, takes away one of the tokens in this pile, and separates the remaining ones into two non-empty piles of arbitrary size. Bob […]

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## Le Monde puzzle [#965]

June 14, 2016## Le Monde puzzle [#964]

June 2, 2016A not so enticing Le Monde mathematical puzzle: Find the minimal value of a five digit number divided by the sum of its digits. This can formalised as finding the minimum of N/(a+b+c+d+e) when N writes abcde. And solved by brute force. Using a rough approach to finding the digits of a five-digit number, the […]

## Le Monde puzzle [#960]

April 28, 2016An arithmetic Le Monde mathematical puzzle: Given an integer k>1, consider the sequence defined by F(1)=1+1 mod k, F²(1)=F(1)+2 mod k, F³(1)=F²(1)+3 mod k, &tc. [With this notation, F is not necessarily a function.] For which value of k is the sequence the entire {0,1,…,k-1} set? This leads to an easy brute force resolution, for […]

## Le Monde puzzle [#959]

April 20, 2016Another 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 […]

## Le Monde puzzle [#958]

April 11, 2016A 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 […]