## Le Monde puzzle [#1144]

**T**he weekly puzzle from Le Monde is again using 2020 but not R!

Two teams involve a prime total number m of participants, with each player getting between 0 and 100 points. The total score for both teams is 2020, with team B less than team A on average. A single transfer from A to B increases the average scores for both A and B by 1/2. What is the difference of the averages? The transfer(ed) player, Camélia, had 5 points less than the average score for A. What was the score of Camélia?

but I could not find a brute force solution and ended up finding that 2×2020=2x2x5x101 is a multiple of m, which leaves only

m=101

as the possible number of players. Which almost immediately leads to a difference of m/2 between the average scores. And then almost as immediately to Camélia’s score being 60. If one really needed an R function

k=function(a){((C<-71-a)>0)&(C+(a-1)/2<102) &(C-((102-a)/2)>0)&(C+5==(C+(a-1)/2))}

does return a=11 but this is 100% useless!

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