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 […]

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## Le Monde puzzle [#1028]

November 16, 2017## Le Monde puzzle [poll]

November 1, 2017As 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!)

## Le Monde puzzle [open problem]

October 23, 2017What should have been the last puzzle in Le Monde competition turned out to be an anticlimactic fizzle on how many yes-no questions are needed to identify an integer between 1 and 1025=2¹⁰+1 and an extension to replies possibly being lies… What is much more exciting is that voting puzzle #1021 got cancelled because the […]

## Le Monde puzzle [#1024]

October 10, 2017The penultimate and appropriately somewhat Monty Hallesque Le Monde mathematical puzzle of the competition! A dresser with 5×5 drawers contains a single object in one of the 25 drawers. A player opens a drawer at random and, after each choice, the object moves at random to a drawer adjacent to its current location and the drawer […]

## Le Monde puzzle [#1022 & #1023]

September 29, 2017Another Le Monde mathematical puzzle where I could not find a solution by R programming (albeit one by cissors and papers was readily available!): An NT is a T whose head (—) is made of 3 50×50 squares and whose body (|) is made of N 50×50 squares. What is the smallest possible side of […]