🇺🇸 Chad Qian

The Countdown Round

MATHCOUNTS is decided in two stages, and the second is the one an audience can watch. Competitors first sit a written examination across a multi-day event; the leaders then go into the Countdown Round, which the organisers describe as lightning-speed and which is closer to a quiz buzzer format than to an examination. Qian competed one-on-one against eleven other top mathletes to reach the end of it.

That structure rewards two different abilities. The written papers measure depth and accuracy over hours. The Countdown Round measures whether a competitor can do the same mathematics in seconds, against another child of the same standard, on a stage, with a buzzer. A national champion has to be good at both, and they are not the same skill.

The coin question

The problem that settled the 2012 title is worth stating in full, because it is a small masterpiece of competition design. A bag of coins contains only pennies, nickels and dimes, with at least five of each. How many different combined values are possible if five coins are selected at random?

Qian answered 21, and it is correct. The reason the question works is that it looks like a counting problem with a messy answer and is in fact a clean one. Five coins drawn from three denominations can be composed in twenty-one ways, and because the values 1, 5 and 10 are spaced as they are, no two of those compositions produce the same total. Every combination gives a distinct sum, so the count of possible values equals the count of combinations.

A competitor who sees that immediately answers in seconds. A competitor who does not can still get there by enumeration, but not fast enough to win a buzzer round. That gap is exactly what the format is built to find.

Carmel, Indiana

Qian was in the eighth grade at Sycamore School in Carmel, a suburb north of Indianapolis. The runner-up, Ashwin Sah, came from Indianapolis as well, which made the 2012 final an all-Indiana affair at the top.

Beyond that, the contemporaneous report used for this page gives nothing: no parents, no coach, no account of how he prepared, no quotation from him. That is normal for coverage of a middle-school mathematics championship, which is written for the event rather than for the competitor.

What MATHCOUNTS is

MATHCOUNTS is a United States middle-school mathematics competition, described by the report as a prestigious academic event, which culminates in a national final. In 2012 it was sponsored by Raytheon, which held the title sponsorship through 2014 and ran it as part of a programme called MathMovesU, intended to raise interest in mathematics and science among school students.

Corporate sponsorship of school competitions is easy to be cynical about and, in this case, hard to fault: the effect is a national circuit that identifies the strongest mathematics students in the country while they are still in middle school and gives them an audience, a stage and a reason to keep going.

Holding the final at a Disney resort is part of the same logic. A child who wins a national mathematics title should be treated, for one weekend, the way a child who wins a national sports title is treated.

What is documented, and what is not

Firm: Qian was an eighth-grader at Sycamore School in Carmel, Indiana; he won the 2012 Raytheon MATHCOUNTS National Competition, held on 11 May 2012 at the Walt Disney World Swan and Dolphin Resort in Lake Buena Vista, Florida; the field was more than 200 middle-school students; he took the title in the Countdown Round against eleven other finalists; the deciding question concerned five coins drawn from a bag of pennies, nickels and dimes and the answer was 21; the runner-up was Ashwin Sah of Indianapolis.

Not documented: his age and birth year, his parents, his coach or team, how he prepared, any quotation from him, the prize he received, and what he has done since 2012. The single contemporaneous report used here is an event write-up, and it is silent on all of it.