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Le Monde puzzle [#875]

July 12, 2014

I learned something in R today thanks to Le Monde mathematical puzzle: A two-player game consists in A picking a number n between 1 and 10 and B and A successively choosing and applying one of three transforms to the current value of n n=n+1, n=3n, n=4n, starting with B, until n is larger than […]

Le Monde puzzle [#872]

June 28, 2014

An “mildly interesting” Le Monde mathematical puzzle that eventually had me running R code on a cluster: Within the set {1,…,56}, take 12 values at random, x1,…,x12. Is it always possible to pick two pairs from those 12 balls such that their sums are equal? Indeed, while exhaustive search cannot reach the size of the […]

Le Monde puzzle [#869]

June 8, 2014

An uninteresting Le Monde mathematical puzzle: Solve the system of equations a+b+c=16, b+c+d=12, d+c+e=16, e+c+f=18, g+c+a=15 for 7 different integers 1≤a,…,g≤9. Indeed, the final four equations determine d=a-4, e=b+4, f=a-2, g=b-1 as functions of a and b. While forcing 5≤a, 2≤b≤5, and  7≤a+b≤15. Hence, 5 possible values for a and 4 for b. Which makes […]

Le Monde puzzle [#868]

June 1, 2014

Another permutation-based Le Monde mathematical puzzle: Given the integers 1,…n, a “perfect” combination is a pair (i,j) of integers such that no other pair enjoys the same sum. For n=33, what is the maximum of perfect combinations one can build? And for n=214?  A rather straightforward problem, or so it seemed: take the pairs (2m,2m+1), their […]

Le Monde puzzle [#865]

May 6, 2014

A Le Monde mathematical puzzle in combinatorics: Given a permutation σ of {1,…,5}, if σ(1)=n, the n first values of σ are inverted. If the process is iterated until σ(1)=1, does this always happen and if so what is the maximal  number of iterations? Solve the same question for the set {1,…,2014}. I ran the following basic R […]

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