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Le Monde puzzle [#977]

October 3, 2016

A mild arithmetic Le Monde mathematical puzzle: Find the optimal permutation of {1,2,..,15} towards minimising the maximum of sum of all three  consecutive numbers, including the sums of the 14th, 15th, and first numbers, as well as the 15th, 1st and 2nd numbers. If once again opted for a lazy solution, not even considering simulated […]

Le Monde puzzle [#967]

September 30, 2016

A Sudoku-like Le Monde mathematical puzzle for a come-back (now that it competes with The Riddler!): Does there exist a 3×3 grid with different and positive integer entries such that the sum of rows, columns, and both diagonals is a prime number? If there exist such grids, find the grid with the minimal sum? I […]

Le Monde puzzle [#965]

June 14, 2016

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 […]

Le Monde puzzle [#964]

June 2, 2016

A 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, 2016

An 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 […]