# Distinct

## Definition

**Distinct** is a commonly used word in mathematics competitions meaning different.

## Examples

- Distinct numbers are numbers which are not equal to each other.
- Distinct sets are sets which are not equal to each other.
- Distinct polygons are polygons which are not congruent to each other.
- Distinct objects are objects which are distinguishable

## Problems

### Introductory

- Let the letters ,,,,, represent distinct digits. Suppose is the greatest number that satisfies the equation

- What is the value of ?
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### Intermediate

- Call a positive integer extra-distinct if the remainders when is divided by and are distinct. Find the number of extra-distinct positive integers less than .

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### Olympiad

- Given any set of four distinct positive integers, we denote the sum by . Let denote the number of pairs with for which divides . Find all sets of four distinct positive integers which achieve the largest possible value of .

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