Given a black-box function f(x) which take a value x and output true for \$p(x)\$, an unknown continious monotone function(not knowing even whether it's increasing), probable; and false otherwise. Output an infinite sequence \$a_n\$ such that \$\lim_{n\rightarrow \infty}p(a_n)=0.5\$. You can assume that the result exists and \$\lim_{n\rightarrow \infty}a_n\$ lay in \$(0,1)\$.
A possible solution:
for i=1..infty
S = [i/2] * i
for j=0..i-1
for k=1..i
if f(j/i)
S[j]--
print minPos([t*t for t in S])/i