**S**ince I have resumed my R class, I will restart my resolution of ** Le Monde** mathematical puzzles…as they make good exercises for the class. The puzzle this week is not that exciting:

Find the four non-zero different digits a,b,c,d such that abcd is equal to seven times the sum of all two digit numbers made by picking without replacement two digits from {a,b,c,d}.

The (my) dumb solution is to proceed by enumeration

for (a in 1:9){ for (b in (1:9)[-a]){ for (c in (1:9)[-c(a,b)]){ for (d in (1:9)[-c(a,b,c)]){ if (7*33*sum(c(a,b,c,d))==sum(10^(0:3)*c(a,b,c,d))) print(c(a,b,c,d)) }}}}

taking advantage of the fact that the sum of all two-digit numbers is (30+4-1) times the sum *a+b+c+d*, but there is certainly a cleverer way to solve the puzzle (even though past experience has shown that this was not always the case!)