## Math Problem Writer ♦ Confidence Builder Math Competition Problems

The problems on this page are Difficulty Level 1 problems written by Douglas Twitchell. These problems are confidence builders. Most math competitions have a few problems that the average student can solve readily with knowledge of the subject area. Brief (not complete) solutions are shown in green, leaving the reader to work through the logic.

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**1.1**

In a triangle, the measures of the angles are x + 10, 3x - 1, and 5x. What is the measure of the largest angle?

- For a student with basic subject knowledge in geometry, this is a simple algebraic equation. Answer is
**95 degrees**

**1.2**

Find the average of all the integers x for which 2x - 5 > 11 and x + 3 < 20

- Combining two inequalities with 'and' gives x>8 and x<17. The average of all the integers from 9 to 16 is
**12.5**.

**1.3**

If a number is added to one more than that number, and then one less than the original number is subtracted from the sum, the result is 21. What is the original number?

- Algebraically, this problem is easy to set up and solve. The biggest challenge is interpreting the wording of the problem. Answer:
**19**

## Difficulty Samples

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