Trivia Done Right

We had our interns search through huge stacks of transcripts in order to write today’s question. Tasked to discover current or recent world leaders who hold PhDs, they came up with an impressive list that includes

• Indian Prime Minister Manmohan Singh, PhD (Oxford ‘62, Economics)
• German Chancellor Angela Merkel, PhD (Physical Chemistry, Leipzig University ‘78)
• Belgian Prime Minister Elio di Rupo, PhD (University of Mons ‘78, Chemistry)
..which leads us to today’s question.

List the U.S. Presidents who held (or perhaps hold) a PhD. For this question, we’re excluding honorary degrees, so only consider earned PhDs when answering.

The Statistical Graphics department has been working overtime to produce this chart. Someone should tell them that we don't pay for overtime.

Can you tell what this chart represents?

Since it’s π day, and March Madness Time, let’s look at some math from three historical points of view

The NCAA tournament has 68 teams in it. How many games are required to determine the champion?

The Greeks would have looked at the problem from a geometrical point of view. They probably would have drawn a bracket, just like the one you may be filling out, and counted the games. The end. No analysis, no work to let them solve the problem for a different number of teams.

We know a lot of Egyptian mathematics, based on archeological findings like the Rhind Papyrus and The Egyptian Mathematics Leather Roll (I didn’t make that up). Much of their mathematics used numbers in tables, and they’d probably do something like making a table of games needed for various sizes tournaments:
# teams Games needed
2 1
3 2
4 3
5 4
⋮ ⋮
68 67
This, 67 Games this time. Note this would give them the answer for any number of games, but would require repeatedly building this for any other number of games, and this approach gives no insight as to why the math works out this way.

A modern mathematician would approach the problem in a third way.
Assume there are n teams in the tournament.
1. Each game produces two things: one winner, and one loser. There is no other outcome.
2. The tournament ends when one and only one team has the value winner.
3. Since only one team has the value winner, there must be n – 1 teams with the value loser.
4. Since each game produces one loser, n – 1 games are required. Written as a relation with T(n) representing a tournament with n competing teams, T(n)=n – 1.
So, 68 teams require 67 games. ∎
This solution results in a formula derived from known principals. Therefore this formula can be used for any number of games AND can be used in future proofs because of its logical foundation.

We here at Trivia Done Right headquarters take a break to play HQ. The Washington Post has something to tell us.

Diving into HQ Trivia: The toughest rounds, the best time to play and how some users beat the odds The live mobile game show’s popularity has soared since launching in August. But what makes winners and losers? Data collected from the game reveals some intriguing bits of human behavior exhibited by the millions now playing.