Question 13
Call finite sets of integers $S$ and $T$ *cousins* if
• $S$ and $T$ have the same number of elements,
• $S$ and $T$ are disjoint, and
• the elements of $S$ can be paired with the elements of $T$ so that the elements in each pair differ by exactly $1.$
For example, $\{1, 2, 5\}$ and $\{0, 3, 4\}$ are cousins. Suppose that the set $S$ has exactly $4040$ cousins. Find the least number of elements the set $S$ can have.
• $S$ and $T$ have the same number of elements,
• $S$ and $T$ are disjoint, and
• the elements of $S$ can be paired with the elements of $T$ so that the elements in each pair differ by exactly $1.$
For example, $\{1, 2, 5\}$ and $\{0, 3, 4\}$ are cousins. Suppose that the set $S$ has exactly $4040$ cousins. Find the least number of elements the set $S$ can have.