JBMO-SL 2016 N2

Find the maximum number of natural numbers $x_{1}, x_{2}, \ldots, x_{m}$ satisfying the conditions:

a) No $x_{i}-x_{j}, 1 \leq i<j \leq m$ is divisible by 11 ; and

b) The sum $x_{2} x_{3} \ldots x_{m}+x_{1} x_{3} \ldots x_{m}+\cdots+x_{1} x_{2} \ldots x_{m-1}$ is divisible by 11 .