## Problem 4

A telephone network has all customer numbers formed of ten digits. What is the maximum number of customers the network can have, knowing that the phone numbers meet the following conditions: the first three digits are in the order $0,7,4$ and the fourth digit is 2 or 6?

Problems selected by Prof. Copil Olimpia

Note: a) The actual working time is two hours.

b) All problems are mandatory.

c) Each problem is scored from 0 to 7.

## NATIONAL MATHEMATICS OLYMPIAD

Local stage - 15.02.2014

## 5th Grade

## Grading Rubric
## Problem 4

Phone numbers have the form 0742 or 0746

Any of the 6 free positions can be occupied by one of the 10 digits

There are $10^{6}$ ways to occupy the 6 free positions

(3p)

There are $2 \cdot 10^{6}$ phone numbers having the required form

Note: a) Each examiner awards an integer number of points.

b) Any other correct solution is graded accordingly.