Each of the digits $1,2,3,4,5,6$ is used exactly once in forming the $3$-digit integers $X$ and $Y$. How many possible values of $X+Y$ are there if $|X-Y|=111?$

Two boys and three girls are going to sit around a table with $5$ different chairs. If the two boys want to sit together, in how many possible ways can they be seated?

What fraction of all the $10$-digit numbers with distinct digits have the property that the sum of every pair of neighboring digits is odd?

qwertyytrewq Apr 23, 2021