Christmas gift

It's holiday season and kids are all having winter break. Here is our new problem:

The positive number n is the product of three different prime numbers greater than 2. If the sum of these three prime numbers is also prime, what is the smallest possible value for n?

What is a prime number? A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

I personally encourage students to memorize the prime numbers less than 100, at least less than 30.

See the following chart:

Because we are asking to find the smallest possible value for n, normally we start from the smallest prime numbers greater that 2. Let's first consider, 3, 5 and 7. The sum of these three prime numbers is 15, which is not a prime number, so 3, 5, 7 are not satisfied. We drop 7 and and consider 11 because we still want to keep the n as small as possible. Now we have 3, 5 and 11. The sum of these three numbers is 19. Check the chart above, YAHOO! 19 is a prime number. Then, we know n = 3*5*11 = 165 is the smallest possible value for n.

Another similar triangle problem

Regarding similar triangles, most of the students can memorize the rules. However, they don't know how to apply the rules to solve problems or they even don't have the sense to realize that the problem is about similar triangles.

Let's take look at the following problem from the official practice test.

Real 2013 SAT math problem

One student in my math club shared this real math problem. Thank you.

This is a simple problem for most students. However, there are several concepts I think are important for students.

One SAT OC practice test problem

Let's take a look at the problem:

The official solution is using the slope of line L. However, we can also use similar triangles to solve this problem. 

A math problem from a BC student

I got a problem from a kid of my friend. I want to share with you.

Here is the problem: