+1713 Help please I tried solving this for a week...
Question:
There are several sets of three different numbers whose sum is 15 which can be chosen from {1,2,3,4,5,6,7,8,9}. How many of these sets contain a 5?
Edit: the answer is 4, I just want to know why...
https://artofproblemsolving.com/wiki/index.php/1991_AJHSME_Problems/Problem_11
+129899 I get four sets
{5 1 9}
{5 2 8}
{5 3 7}
{5 4 6}
{5, 5, 5} not possible
(5, 6, 4} repeat set
(5, 7, 3} repeat set
(5, 8, 2} repeat set
(5, 9 , 1} repeat set
+2864 These problems are really brute force, there is no real clever way. I only just listed all possible combinations
HOWEVER, notice in CPhill's answer.
5 19
5 2 8
5 3 7
5 4 6
Since ALL the sets contain a 5, we just subtract 5 from 15.
So we need TWO terms in a set and they add up to 10, and also are unique.
This is quite easy.
1 9
2 8
3 7
4 6
5 5 (doesnt work because cannot repeat digit)
+1713 Brute force!
Oh no I was hoping for a trick... :(
But your answers are still great!
+2864 I mean the trick is to find all unique pairs that added up to 10. But its KIND OF a trick.
+2864 I have a bad habit of not recognizing tricks, and usually brute force everything... Only when I review do I realize the clever tricks to problems. This is why I take so long on AMC competitions.
The worst kind of problems are the ones where you have to know a formula to solve, because there is no cleverness and you know it or you dont know it.
+1713 I finished the AMC8.
But you know that pamphlet...
I put my answers there instead of in the bubble sheet...
XD
So I have to retake it...
+2864 OOOFF !!!
Thats a massive OOOOOFFFFF
I mean, AMC 8 is a very important test for me. And my parents and my teachers are worried on how I do this year, so seeing what happened to you made it seem scary.
+1713 yeah but there is a problem-I skipped grades so its confusing...
Im in 8th grade now so im so confused.
still taking it
XD
