Greatest Integer Function and Radicals in one problem? Be still my beating heart. A problem where intuition works best? Awesome. Similar triangles masquerading as a tough problem. Wow!
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 20, answer 21 and answer 22.