Problem 2. A three-digit natural number divided by its reverse gives a quotient of 2 and a remainder of 100, and the difference between the hundreds digit and the units digit of the number is equal to 4. Find the number.

Mihai Ilie, Slatina
## Solution and marking scheme

$\overline{a b c}=2 \cdot \overline{c b a}+100$ ..... (2p)
$98 a=10 b+199 c+100$ ..... (1p)
$a=c+4 \Rightarrow 10 b+101 c=292$ ..... (2p)
$b=9, c=2 \Rightarrow \overline{a b c}=692$ ..... (2p)