# Four Digits

**Number Theory**Level 2

Find a Four Digit Number, whose-

- Second and Third digits are equal.
- Fourth digit is twice the first digit, and
- 1st and 2nd digits combined is half of 3rd and 4th digits combined.

For example, if the number is \( \overline{xyyz} \), then we have \( 2\times x = z \) and \( 2 \times \overline{xy} = \overline{yz} \).

Note: \( \overline{xy} \) is equal to \( 10 x + y \). It is not equal to \( x\times y \).