# Buzz Contest Rules

The Buzz Contest is the mathematical equivalent of a spelling bee. Its
1992 revival at Texas A&M University marked the 10^{th} anniversary of the
last time Texas high school students had played the game at the 1982 Lamar Mathematics Day
competition. Since then, this contest has been a popular feature of the Texas A&M
University Math Tournament.

The general structure of the game is as follows: The students line up and count off. The first student calls N, where N is an integer between 1 and 20, which is randomly determined, the second student calls N+1, and so on. If a student gets his or her number wrong, he or she is eliminated and the next student in line must say the number the previous student should have said. All of this is done very quickly; a student may be eliminated for "delay of game".

So far, the game as described is too easy. To complicate matters, some numbers are designated as special. When it is a student's turn to call out a number and that number is special, the student should not say the number, but should instead say some combination of codewords relating to the number. The codewords and their meanings are:

**BANG: **The number contains a 5 (in its base-10 representation)
or is divisible by 5.

**BUZZ: **The number contains a 7 (in its base-10 representation)
or is divisible by 7.

**CRASH: **The number is prime.

**FIBBI:** The number is a Fibonacci number. The Fibonacci
numbers are constructed as follows:

F_{1} = 1, F_{2 }=
1 and F_{n+2} = F_{n+1}
+ F_{n. }. So F_{3 }
= 2 , F_{4 }= 3, F_{5 }=
5, etc.

Thus, the first 6 Fibonacci numbers are 1, 1, 2, 3, 5, and 8.

**POP: **The number is the product of two distinct primes.

**SQUAWK**: The number is the sum of two squares. For example,
9=3^{2} + 0^{2}, and 5 = 2^{2}
+ 1^{2}

**WHIZZ: **The number is square-free (is not divisible by a perfect
square other than 1).

**ZIP: **The number is a perfect *k* th power with
*k* greater than or equal to 2.

These codewords are not all in force at the beginning, but are introduced or removed gradually at the will of the moderator and in any order. For example, suppose Michael, Deena, Christa, Heath and Amy are still in the game. The codewords Fibbi, Bang, Pop and Zip are in force, and it is Deena's turn on number 29. The sequence would sound something like this.....

**Deena: **29

**Christa: **Bang

**Heath: **31

**Amy:** 32 (This is wrong; Amy is eliminated.)

**Michael: **Zip

**Deena:** Pop

**Christa:** Pop, Fibbi

**Heath: ** Bang (This is wrong; Heath is eliminated.)

**Amy: ** Bang Pop (The next number is 36.)

Please note that a lot of students are likely to fall in the 40's and 50's as it is very easy to lose track of what number we're on. The proctor will not advise the students. It is the responsibility of each student to keep track for themselves even as others are eliminated.

The discussion at this link should help you determine which, if any, of the code words apply to a particular number.

The last remaining student must say correctly what the second-to-last student should have said to win the contest. Trophies will be awarded to the first and second place finishers.