Problem $3.$ Ulam's problem ask for the number of queries required to find $x,$ supposing that the first person is allowed to lie exactly once.

a$.$ Option $1$: $[$Ask each Question Twice!$]$ Show that by asking each question twice, given a number $x$ and a set with $n$ elements, and asking one more question when we find the lie. Ulam's problem can be solved in at most $2lo{g}_2(n)+1$ queries. Demonstrate this process by finding the $4$ in the following lists $($you may choose when the 'lie' occurs$)$

$\backslash$table$[[1,3,7,4,2,0,6,5]]$

$\backslash$table$[[8,6,7,5,3,0,9,11,13,17,4,2,15,10,12,1]]$