## Math Problem Writer ♦ Moderate Math Competition Problems

The problems on this page are Difficulty Level 2 problems written by Douglas Twitchell. These are the moderate difficulty competition problems. Think of these as filler problems--they're not so easy that *everyone* will get them, but not so difficult that they'll make the cream of the crop stand out. Brief (not complete) solutions are shown in green, leaving the reader to work through the logic.

Click here for more information about problem writing services, or click here to contact us about your league's competition needs.**2.1**

How many 3 digit numbers have no repeated digits?

- This problem is more time consuming than difficult. Tests the student's ability to keep track of 'details'. Answer is
**648**

**2.2**

If x^{2} + y^{2} = 100, and xy = 18, find the value of x - y.

- Students can 'grind it out' painfully, but a short cut--if they spot it--will give the answer in seconds. The solution is
**8 or -8**

**2.3**

In a triangle, the sum of two of the angles is equal to the third. If the lengths of the two longer sides are 12 and 13, what is the length of the shortest side?

- The biggest challenge here is recognizing that although it is not directly stated, this is a right triangle. Answer is
**5**

## Difficulty Samples

- Difficulty Level 1
- Difficulty Level 2
- Difficulty Level 3
- Difficulty Level 4