Le Monde puzzle [38]

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 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)))

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!)

5 Responses to “Le Monde puzzle [38]”

  1. Where does the 7 come from? The sum of all two digit numbers made by picking without replacement two digits from {a,b,c,d} is 33*sum(a,b,c,d). How does the multiplier scale up to 231?

    Thank you!

    • Sorry, it has been a while since I posted this entry and I had no memory whatsoever of the problem! Checking on Robin’s blog entry, I have realised I omitted the multiplication by 7. The question now stands corrected, thank you!

  2. […] Monde puzzle [34] Since the puzzle in this week (-end) edition of Le Monde is not (easily) solvable via an R program, I chose to go […]

  3. Not much different but checks only a small set..

    mysets <-permutations(9, 4)

    # now check these 7 possibilities
    for(i in 1:length(possible.sol)){

  4. […] on PIN number By robinryder Now that the new school year has started, Christian Robert has picked up solving the Le Monde mathematical puzzles using R again, which leads me to solving them without […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: