Question 18
Let $t$ be a non-zero real number and $n$ be a positive integer. Let $a_1, a_2, \dots, a_{2n-1}$ be real numbers (not necessarily distinct). Prove that there exist indices $i_1 \lt i_2 \lt \dots \lt i_n$ such that $a_{i_k} - a_{i_{l}} \neq t$ for any $1 \le k, l \le n$.