Surprising Solution!

Here is a very simple problem with an even simpler solution. Try the problem yourself and see whether you fall into the “majority-solvers” group.

A single elimination (one loss and the team is eliminated) basketball tournament has 25 teams competing. How many games must be played until there is a single tournament champion?

Typically, the majority-solvers will begin to simulate the tournament, by taking two groups of 12 teams, playing the first round, and thereby eliminating 12 teams (12 games have now been played). The remaining 13 teams play, say 6 against another 6, leaving 7 teams in the tournament (18 games have been played now). In the next round, of the 7 remaining teams, 3 can be eliminated (21 games have so far been played). The four remaining teams play, leaving 2 teams for the championship game (23 games have now been played). This championship game is the 24th game.

A much simpler way to solve this problem, one that most people do not naturally see, is to focus only on the losers and not on the winners as we have done above. If asked the key question: “How many losers must there be in the tournament with 25 teams in order for there to be one winner?” The answer is simple: 24 losers. How many games must be played to get 24 losers? Naturally, 24. So there you have the answer, very simply done.

Now most people will ask themselves, “Why didn’t I think of that?” The answer is, it was contrary to the type of training and experience we have had. Making youngsters aware of the strategy of looking at the problem from a different point of view may sometimes reap nice benefits, as was the case here. One never knows which strategy will work; just try one and see!