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Le Monde puzzle [38]

Posted in R, University life with tags , , , on September 30, 2010 by xi'an

Since 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 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 (231*sum(c(a,b,c,d))==sum(10^(0:3)*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!)