Could you please help me with this puzzle that I am not able to find a nice answer to!!
There are 49 cars which race at unique speeds. Also there is a race track in which at maximum 7 cars can be raced together. We need to find the 25th fastest car in the group. We don't have a stop watch to measure time (so we can only measure the relative speed of each car w.r.t the 6 other cars in a race). What is the least number of races that would be needed?
Can't you iteratively divide the pool by determining the exact position of a car?
Pick a car at random to pivot by Run through each of the other 48 cars, racing them in groups of 6 against the pivot car You know now the pivot car's exact position.
Now run the same process on the portion of the set that you know to include position 25 in it. If you have less than seven elements in the remaining partition, it is simple to determine.
The worst case performance of this is truly horrendous, but could be mitigated by picking successive pivots in some semi-intelligent way.