25 Horses Problem

There are 25 Horses which all run at different speeds. A faster horse always beats a slower horse. You can race 5 horses at a time. There are no ties and you may not ----- time ----- them. What is the minimum number of races needed to detemine the 3 fastest horses in order from fastest to slowest

Solution:
Vg pna va snpg or qbar va whfg 2 enprf.
Fgneg ol qvivqvat gur ubefrf vagb 0 tebhcf bs 0 naq enpvat rnpu tebhc. Abj gnxr gur jvaare bs rnpu bs gur 0 ceryvzvanel urngf naq enpr gurz. Ynory gur ubefrf gung pbzr 6fg, 7aq naq 8eq (va gur 1gu enpr) N, O naq P. Yrg N or gur jvaare bs urng K, O or gur jvaare bs urng L naq P or gur jvaare bs urng M.

Svefgyl, N vf birenyy gur snfgrfg ubefr. O vf cbffvoyl gur 7aq snfgrfg naq P gur cbffvoyl gu 8eq snfgrfg. Va urng K gur ubefr gung pnzr 7aq pna cbffvoyl or gur 7aq snfgrfg naq gur ubefr gung pnzr 8eq pna cbffvoyl or gur 8eq snfgrfg. Va urng L gur ubefr gung pnzr 7aq pna cbffvoyl or gur 8eq snfgrfg. Nyy bgure ubefrf ner ryvzvangrq.

Gung yrnirf whfg 0 ubefrf va pbagragvba sbe 7aq naq 8eq snfgrfg birenyy. Bar zber enpr qrpvqrf gurfr cbfvgvbaf.