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Le Monde puzzle [#1016]

July 16, 2017

An even more straightforward Le Monde mathematical puzzle that took a few minutes to code in the train to Cambridge: Breaking {1,…,8} into two sets of four integrals, what is (or are) the division into two groups of equal size such that the sums of the squared terms from each are equal? Same question for […]

Le Monde puzzle [#1015]

July 10, 2017

A combinatoric Le Monde mathematical puzzle: A game with N questions and N players is such that each question is solved by all players but three, while any pair of players fails to jointly solve the N questions. What is the maximal number N of players? N=6;play=1;besz=1 while ((besz>0)||(play<N)){ gamz=matrix(1,N,N) for (qez in 1:N) gamz[qez,sample(1:N,3)]=0 […]

Le Monde puzzle [#1014]

June 30, 2017

One of those Le Monde puzzles where a computational solution seems out of reach: given 2N batteries out of which N are charged, how many tests of pairs of batteries are necessary to find a working pair? I first tried a brute force recursive resolution checking all (2N-1)N orders of pairs over all (2N)! permutations […]

Le Monde puzzle [#1013]

June 23, 2017

A purely arithmetic Le Monde mathematical puzzle: An operation þ applies to all pairs of natural integers with the properties 0 þ (a+1) = (0 þ a)+1, (a+1) þ (b+1)=(a þ b)+1, 271 þ 287 = 77777, 2018 þ 39 = 2018×39 Find the smallest integer d>287 such that there exists c<d leading to c þ d = c x d, […]

Le Monde puzzle [#1012]

June 14, 2017

A basic geometric Le Monde mathematical puzzle: Take a triangle ABC such that the side AB is c=42 long, each side has an integer length, and the area is 756. Given an inner point D, draw three lines parallel to the three sides of ABC through D in order to construct three triangles with common […]