Brain Teasers
Ordered Triple
Find the number of ordered triples (A, B, C) where A, B and C are positive integers, A is a factor of B, A is a factor of C, and A+B+C=30.
Hint
If A is a factor of both B and C, A must be a factor of the three numbers' sum 30.Answer
If A=1, then the possibilities are B=1, C=28; ..., B=28, C=1, 28 possibilities;If A=2, then the possibilities are B=2, C=26; ..., B=26, C=2, 13 possibilities, 41 accumulated;
If A=3, then the possibilities are B=3, C=24; ..., B=24, C=3, 8 possibilities, 49 accumulated;
If A=5, then the possibilities are B=5, C=20; ..., B=20, C=5, 4 possibilities, 53 accumulated;
If A=6, then the possibilities are B=6, C=18; ..., B=18, C=6, 3 possibilities, 56 accumulated;
If A=10, then the only possibility is B=10, C=10, 57 possibilities accumulated.
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
I thougth we were supposed to find just 1 answer.
Fresh. Personally, I like to be confronted by a question. As an example, "How many ordered triples are there such that etc.?"
(1, 10, 19) (2, 10, 1 (5, 10, 15) & (10, 10, 10)
(1, 10, 19) (2, 10, 1 (5, 10, 15) & (10, 10, 10)
To post a comment, please create an account and sign in.
Follow Braingle!