## Le Monde puzzle [#825]

**T**he current puzzle is the last one before the summer break and not exciting enough to take along:

Take the first ten digits, create five pairs out of those, and for each pair (x,y) derive the quantity (min(x,y)+1.5max(x,y)). What is the collection of pairs that maximises the product of those quantities?

**I** wrote the following R code in the train back from Annecy:

res=0 bonus=1.5 for (t in 1:1000){ x=matrix(sample(1:10),ncol=2) mix=apply(x,1,min);mox=apply(x,1,max) rex=prod(mix+bonus*mox) if (rex>res){ print(x) res=rex} }

and got:

[,1] [,2] [1,] 4 7 [2,] 5 6 [3,] 8 3 [4,] 2 9 [5,] 1 10

**T**hus the sum of the pairs is always equal to 11. And by changing bonus you can check this is true for all values of the coefficient that are larger than one (one included).

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