## Task A-4.4.

Determine the smallest multiple of 84 that, in decimal notation, contains only the digits 6 and 7.
## Solution.

A number is divisible by 84 if and only if it is divisible by 3, 4, and 7.

Since the desired number must be divisible by 3, the number of digit 7s must be divisible by 3. 1 point

The desired number must be even, so it must end with 6. 1 point

Since the desired number is divisible by 4, it must end with 76. 1 point

We conclude that the desired number contains at least 3 digits $7. \quad 1$ point

Numbers that satisfy the given conditions are 7776, 67776, 76776, 77676, ...

Since the numbers 7776 and 67776 are not divisible by 7, 1 point

and the number 76776 is, we conclude that the answer is 76776.

1 point