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Le Monde puzzle [#1036]

January 4, 2018

An arithmetic Le Monde mathematical puzzle to conclude 2017: Find (a¹,…,a¹³), a permutation of (1,…,13) such that a¹/a²+a³=a²+a³/a³+a⁴+a⁵=b¹<1 a⁶/a⁶+a⁷=a⁶+a⁷/a⁷+a⁸+a⁹=a⁷+a⁸+a⁹/a⁵+a⁹+a¹⁰=b²<1 a¹¹+a¹²/a¹²+a¹³=a¹²+a¹³/a¹³+a¹⁰=b³<1 The question can be solved by brute force simulation, checking all possible permutations of (1,…,13). But 13! is 6.6 trillion, a wee bit too many cases. Despite the problem being made of only four constraints […]

Le Monde puzzle [#1033]

December 19, 2017

A simple Le Monde mathematical puzzle after two geometric ones I did not consider: Bob gets a 2×3 card with three integer entries on the first row and two integer entries on the second row such that (i) entry (1,1) is 1, (ii) summing up subsets of adjacent entries produces all integers from 1 to […]

Le Monde puzzle [#1029]

November 22, 2017

A convoluted counting Le Monde mathematical puzzle: A film theatre has a waiting room and several projection rooms. With four films on display. A first set of 600 spectators enters the waiting room and vote for their favourite film. The most popular film is projected to the spectators who voted for it and the remaining […]

Le Monde puzzle [#1028]

November 16, 2017

Back to standard Le Monde mathematical puzzles (no further competition!), with this arithmetic one: While n! cannot be a squared integer for n>1, does there exist 1<n<28 such that 28(n!) is a square integer? Does there exist 1<n,m<28 such that 28(n!)(m!) is a square integer? And what is the largest group of distinct integers between […]

Le Monde puzzle [poll]

November 1, 2017

As the 25 Le Monde mathematical puzzles have now been delivered (plus the extraneous #1021), the journal is asking the players for their favourites, in order to separate ex-aequos. For readers who followed the entire sequence since puzzle #1001, what are your favourite four puzzles? (No more than four votes!)