We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
57
9
avatar+1342 

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

 Aug 29, 2019
edited by tommarvoloriddle  Aug 30, 2019
 #1
avatar+103148 
+2

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

 

 

cool cool cool

 Aug 30, 2019
 #2
avatar+1129 
+5

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)

CalculatorUser  Aug 30, 2019
edited by CalculatorUser  Aug 30, 2019
edited by CalculatorUser  Aug 30, 2019
 #3
avatar+1342 
+3

Brute force! 

Oh no I was hoping for a trick... :(

 

But your answers are still great!

tommarvoloriddle  Aug 30, 2019
 #4
avatar+103148 
+1

Thanks, CU  and Tom  !!!

 

 

cool cool cool

CPhill  Aug 30, 2019
edited by CPhill  Aug 30, 2019
 #5
avatar+1129 
+4

I mean the trick is to find all unique pairs that added up to 10. But its KIND OF a trick.

CalculatorUser  Aug 30, 2019
 #6
avatar+1129 
+3

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.

CalculatorUser  Aug 30, 2019
 #7
avatar+1342 
0

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...

tommarvoloriddle  Aug 30, 2019
edited by tommarvoloriddle  Aug 30, 2019
 #8
avatar+1129 
+2

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.

CalculatorUser  Aug 30, 2019
 #9
avatar+1342 
0

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

tommarvoloriddle  Aug 30, 2019

19 Online Users

avatar