Fuzzy Math

Trey Reely | October November 2020

 His low, gravelly voice rumbled across the room like an earthquake. “Trey Reely. Do you have your homework?” “Yes, Mr. Powell,” I would reply meekly. Mr. Powell didn’t just teach algebra, he preached it. He held his tattered algebra text like it was Holy Scripture and spoke religiously about algebraic expressions and functions in a way usually reserved for a fire and brimstone sermon. I think he would be proud to know that I’m applying the little math knowledge I have retained to my musical pursuits. See if you can solve these brain teasers.

A concert band has seven trumpet players. The band is performing a three-movement work that calls for straight mutes in each movement. Two players accidentally drop their mutes during the first movement, and three more accidentally drop theirs during the second movement. How many trumpet players are left to drop their mutes in the third movement?

    None. The other two forgot to bring their mutes.

The director of a 100-member marching band excitedly mic drops from a 30-foot band tower following the setting of the final set. How many band members cheer as it hits the ground?

    99 – All but the majorette who didn’t get a solo.

How do you calculate the number of flag-line members in a band without seeing the band perform?

    Count the holes in the band room ceiling tiles and divide by two.

A beginning clarinet player chips his reed. How many more chips before he gets a new one?

    No single answer. This is directly proportional to when the band director notices.

What is the common denominator: 82% beginning band registration rate; 80% fundraiser participation rate; 100% dress rehearsal attendance?


An eight-member trombone section has 20 measures of extended rests between rehearsal letters C and D. Then 12 more between letters D and E. Then 8 more from E to F. How many players will miss the entrance at letter F?

    None, because they all entered at letter E, and the director gave them a dirty look before cueing them at letter F.

The district band budget is $5,000. The district football budget is $25,000. How many candy bars must the band sell to equal the athletic budget?

    Based on dollar bars sold at 50% profit, the total would be 40,000. However, the band’s budget just dropped while doing the math for this problem, raising the total to 42,000 candy bars.

A percussion section is given six different parts for a concert selection. How many parts will still be available for the second rehearsal?

    Given that all six parts will be left on the music stand, an average of one part will disappear each class period until the next rehearsal. In a seven-period day, that means no music will be available.

A metronome and a typical band performing a march begin at quarter note = 120. Which finishes first?

    The metronome because the band drags the trio.

You are at a band’s halftime show. A clarinet section has 20 members. Clarinet player X is out-of-phase by measure three, with neither foot hitting on the beat. The tempo increases at measure 24, slows and changes to ¾ time at measure 48, then slows again for a majestic ending. How many clarinet players are in step?

    Clarinet player X if the tempo is ju-u-u-u-u-st right.

A band director buys a new set of wind chimes in August. How many bars will be missing from it by May?

    This will depend on the number of performances. Wind chimes are typically dropped every time they are moved, regardless of the age of the ensemble. The only thing that changes is the distance from which the winds chimes crash to the floor. So for four performances, one is looking at probably four drops and one lost bar for every other drop. Therefore, the answer most likely is two. However, the odds increase exponentially if the wind chimes are used during marching band.

A percussionist goes to the percussion cabinet for a triangle beater. What time of year will she have the most options in beater choices?

    The last week of school. There will be more options each month as more and more wind chime bars become available.

There are ten trumpet players in the section. How many of them have a pencil for rehearsal?

    None. They “never” make mistakes.

You are the director of a 114-member band. Your football team is the 12th seed playing the 1st-seed team whose school is located 372 miles away from your school. Your team throws 30 incomplete passes yet scores 50 points, and the opposing team throws 20 incomplete passes yet scores 80 points. The games ends at 11:20 pm. What is the only certainty in this scenario?

    The single place to stop on the way home for a break only has one bathroom.

A band director says “one more time.” How many more times will the band play it?

    As many as he/she feels like it.

What is 1/8 + 2.5/4 + 1.5/4 + 2/4 + 2/4 + 3/8 + ¼?

    Measures 2-8 of “Lord Melbourne” from Grainger’s Lincolnshire Posy.

There are four oboists in a band. The tuning is terrible. According to them, what percentage of the section is at fault?

    Zero. All of the blame should be placed on the reeds.

A jet is taking off near the band room at 140 decibels, an ambulance is driving by with a siren at 120 decibels, a jackhammer is drilling concrete at 110 decibels right outside the band room door, and firecrackers are going off at 160 decibels in the middle of the band room. How many alto saxophone players will have to stop playing for you to hear this?

    Assuming you have eight saxophones, probably seven of them if the remaining one has a bad reed.

It is May. Henry is a beginning trombone player. How many slide positions are available to Henry?

    Five if his right arm is strong enough.

Bonus: A 24-year-old band director making a salary of $30,000 per year that increases $550 annually is offered a job at a company for $60,000 per year with a 5% increase each year, yet declines the offer. Write this in the form of an equation.

    ($60,000y + i) < ($30,000y + z)*L
    y = years taught
    i = 5% salary increase compounded annually over course of your career
    z = $550 per year added each year over the course of your career
    L = love of watching your students grow to love the art of music

    Special thanks to Terry Hogard, Director of Bands at Brookland High School (Arkansas), for his assistance with this article.