The Impossible Question1

:: Context (Would I move Mt. Fuji?) ::


This was one of those moments when I felt at least for a second that I was an older Jim Gibbons (1) in my early thirties, in front of the great William Shockley (2). What really fascinated me was that the reasoning that I had applied for the solution had striking similarity with the reasoning of the then, interviewer (2) and interviewee (1).

The Interview Scene (original excerpt from the book):

Shockley picked up his stopwatch.
There’s a tennis tournament with one hundred twenty-seven players, Shockley began, in measured tones. You’ve got one hundred twenty-six people paired off in sixty-three matches, plus one unpaired player as a bye. In the next round, there are sixty-four players and thirty-two matches.
How many matches, total, does it take to determine a winner?
Shockley started the stopwatch.

Though it’s said think twice (or more) before you do something, I think one needs to understand well “what” one is trying to do rather that worrying “how”, from the word “GO”. I guess that’s how i landed a knock-out in the first round.

Please give it a try if you haven’t, before you read my take on it…

:: My Take On It ::


Shockley was just setting the stage for Gibbons as indicated clearly by the strike-through lines. This is a diversion from the actual problem inducing unwanted complexities to the actual problem problem at hand. Now comes the real kill; the statements underlined will definitely take the interviewee off course on a wild-goose chase (though in this case would definitely lead you to the answer but not quick enough to beat Shockley’s stopwatch), but it discretely conveys the random knock-out nature of the tournament which is a key attribute in determining the solution. So, the final problem statement gets almost reduced to the “italic statements in bold”.

Shockley picked up his stopwatch.
There’s a tennis tournament with one hundred twenty-seven players, Shockley began, in measured tones. You’ve got one hundred twenty-six people paired off in sixty-three matches, plus one unpaired player as a bye. In the next round, there are sixty-four players and thirty-two matches.
How many matches, total, does it take to determine a winner?
Shockley started the stopwatch.

The answer is now lying open in front of you:

:: To determine a fair winner all others would have to be eliminated in this knock-out tournament which leaves us with 126 matches ::

Now the mathematical derivation which Shockley would have liked Gibbons to do based on his underlined statements:

  • 126 players -> 63 matches (A)
  • 064 players -> 32 matches (B)
  • 032 players -> 16 matches (C)
  • 016 players -> 08 matches (D)
  • 008 players -> 04 matches (E)
  • 004 players -> 02 matches (F)
  • 002 players -> 01 matches (G)
Ans: A+B+C+D+E+F+G :: 63+32+16+8+4+2+1 = 126 matches