Welcome to our community

Be a part of something great, join today!

Problem of the week #86 - November 18th, 2013

Status
Not open for further replies.
  • Thread starter
  • Admin
  • #1

Jameson

Administrator
Staff member
Jan 26, 2012
4,052
This problem is geared at younger high school students but is a good introduction to proofs and laying out mathematical arguments.

For real numbers $a,b$ what is $\max \left({a, b}\right) + \min \left({a, b}\right)$? Show all steps in your solution.

Hint:
There are 3 cases to consider.

--------------------
Remember to read the POTW submission guidelines to find out how to submit your answers!
 
  • Thread starter
  • Admin
  • #2

Jameson

Administrator
Staff member
Jan 26, 2012
4,052
Congratulations to the following members for their correct solutions:

1) eddybob123
2) kaliprasad
3) MarkFL

This problem was on one hand very easy but it focuses on making strong mathematical arguments for general situations, which is a great skill to develop at a young age. So if you're in middle school, high school or just starting to get into math I suggest you try this problem before looking at the solution.

Solution (from eddybob123):
Let us consider three cases:

Case 1 $a>b$: It follows that $\max(a,b)=a$ and $\min(a,b)=b$, and their sum is $a+b$.

Case 2 $a<b$: This is the opposite of the first case. We have $\max(a,b)=b$ and $\min(a,b)=a$, and their sum is also $a+b$.

Case 3 $a=b$: Since $a=b$, it does not matter what values we use for $\max(a,b)$ and $\min(a,b)$. Their sum can be represented in either of the forms $2a$, $a+b$, or $2b$.

In all three cases, the sum of the maximum and the minimum of two real numbers is simply the sum of the numbers.
 
Status
Not open for further replies.