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Egyptian fractions [Le Monde puzzle #922]

July 28, 2015

For its summer edition, Le Monde mathematical puzzle switched to a lighter version with immediate solution. This #922 considers Egyptian fractions which only have distinct denominators (meaning the numerator is always 1) and can be summed. This means 3/4 is represented as ½+¼. Each denominator only appears once. As I discovered when looking on line, […]

Le Monde puzzle [#920]

July 23, 2015

A puzzling Le Monde mathematical puzzle (or blame the heat wave): A pocket calculator with ten keys (0,1,…,9) starts with a random digit n between 0 and 9. A number on the screen can then be modified into another number by two rules: 1. pressing k changes the k-th digit v whenever it exists into […]

Le Monde puzzle [#919]

July 19, 2015

A rather straightforward Le Monde mathematical puzzle: Find 3 digit integers x such that the integer created by collating x with (x+1) gives a 6 digit integer that is a perfect square. Easy once you rewrite the constraint as 1000x+x+1 being a perfect square a², which means that x is equal to (a-1)(a+1)/1001, hence that […]

Le Monde puzzle [#913]

June 12, 2015

An arithmetics Le Monde mathematical puzzle: Find all bi-twin integers, namely positive integers such that adding 2 to any of their dividers returns a prime number. An easy puzzle, once the R libraries on prime number decomposition can be found!, since it is straightforward to check for solutions. Unfortunately, I could not install the recent […]

Le Monde puzzle [#910]

May 8, 2015

An game-theoretic Le Monde mathematical puzzle: A two-person game consists in choosing an integer N and for each player to successively pick a number in {1,…,N} under the constraint that a player cannot pick a number next to a number this player has already picked. Is there a winning strategy for either player and for […]

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