• Find two fractions \(a/b\) and \(c/d\), such that the ambiguous number \(x\) sits exactly halfway between them. That is, \[x=\frac{p}{q} = \frac{ad+cb}{2bd}\] subject to the constraint \(2bd<10^8\).
  • The Stern-Brocot tree can be used to systematically generate these fraction pairs.
  • However, because the tree traversal is initiated strictly within the target interval, the pairs straddling the right boundary of \(1/100\) need to be handled explicitly.