# Competition Problems

There are four events to Math-Team-Matics - so really it's a Quadrathalon.

The structure of the competition is:

Team Challenge - open-middle problem that requires collaboration to solve within the time limit.

Individual Challenge - multiple choice problems trying to get at a different perspective than the usual quiz.

Relay Race - quick numerical problems that require the data from the runner before you.

Quiz Bowl - mix of turn-based and toss-up questions pitting one team against another.

Final Quiz Bowl - top two teams in each division face off in a winner takes all match.

Math content that is fair game for the competition is K-8 mathematics, plus high school algebra and geometry.

Here are some sample problems for the different phases. In the competition there will be an emphasis on fun and challenge.

**Team Challenge***Sample*How many numbers from 1 to 20 can you compute using the digit 9 exactly three times and any mathematical operation +, -, x, /, sqrt, factorial, decimal point, etc, but no other numbers or digits. You have to use 9s as digits, not necessarily the number 9, so 9, 99, 9.9, etc. are all fair. Extension: 21-30!

2016 Dodecagon Tiling (thanks to Henri Picciotto)

2015 MacMahon Squares Problem & Squares sheet

2014 Truchet Polygons

2013 Cubic Stairs Pattern

**Individual Test** (Multiple choice)To make this collaborative, we drop the high and the low scores, make a team score with credit for any problem anyone on the team answered correctly, then average that with the three middle scores.

Example: Ten liters of a 30% acid solution are obtained by mixing a 25% solution and a 50% solution. How many liters of the 25% solution must be used? (A) 1 (B) 1.5 (C) 2 (D) 5 (E) 8

2016 Individual Challenge

2015 Individual Challenge

2014 Individual Test

2013 Individual Questions (pdf)

**Relay Race** What is the sixth whole number factor of 144, counting from least to greatest? What is the answer to number 1 multiplied by 2.5? If the answer to number 2 is the amount a consumer pays for a movie and a third of that amount is profit for the theater. How much is profit?

Alex runs a lap in 90 seconds. If Alex ran (answer to number 3) laps, how long will it take him (in minutes)?

Take the answer to number 4, double it, and then add the sum of the first three prime numbers.

If the answer to number 5 is the area of a face on a cube, what is the volume of this cube?

2014 Relay Questions (there was a mistake on one... )

2013 Relays Questions (pdf) (general agreement that John was overzealous on these, but he likes the strong theme to each set.)

**Quiz Bowl**How many days between brothers born on March 19, 2000 and February 27, 2001?The area of a right triangle is 28 cm^2 and one leg is 4cm. How long is the hypotenuse?

2016 Quiz Bowl: Round One, Two, Three and Final (slides); Answers

2015 Quiz Bowl: Round One, Two, Three and Final (slides); Answers

2014 Quiz Bowl: Round One, Two, Three and Final (slides); Answers

2013 Quiz Bowl (4 Rounds; pdf)