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avatar+1709 

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+111438 
+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+2856 
+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+1709 
+1

Brute force! 

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

 

But your answers are still great!

tommarvoloriddle  Aug 30, 2019
 #4
avatar+111438 
+1

Thanks, CU  and Tom  !!!

 

 

cool cool cool

CPhill  Aug 30, 2019
edited by CPhill  Aug 30, 2019
 #5
avatar+2856 
+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+2856 
+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+1709 
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+2856 
+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+1709 
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

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