Mathman 9 -
The Lockbox
Peter Walther, Ben Prekop, Josh Minzlaff, Jason Seivert

At the end of these clues you need to perform a difficult matrix multiplication.  Go to this page to learn how to do this on a free graphics calculator simulator or to do it by hand.  You can actually do this at home before you go hunt for the box.

Go to Brookfield East High School on Lily Road, just north of Burleigh Road.  Park in the northwest corner of the parking lot close to the softball diamonds.  There is a sign there by the path saying buses should park here for visitors to the nature center, so it should be okay to park here as you'll be going through the nature center.  Just to be on the safe side, you might place a note on your dashboard stating you are walking through the nature center and will be back shortly.

You will walk west on the paved path north of the soccer field, but before you do, notice the two gate numbers to the left of the path on the fence surrounding the soccer field.  Record the one on the left as A and the one on the right as B.  A = ______  B = ______

Proceed down the paved path, and you will see a baseball field in front of you where the path curves. Take the average of the three different numbers on the outfield fence and record it as L = ______

Now follow the curve of the paved path south until you go past the small nature building. You will then see the entrance to the nature center on your right.  Stand on the west side of the big tree in the middle of the path.  Take 5 steps west.  Now solve this problem using A and B:

Find the amount, in whole dollars, in a bank account after 2 years, if you invest $150 at an interest rate of (B + 0.5) percent compounded (A divided by 2) times a year.  Answer= ______

Take the path on this bearing until you reach the next intersection.  Continue facing on that bearing, and while at the intersection, look at the pine tree ahead of you.  You should see a red number somewhat up the tree.  Let this number be C = ______

Then solve the following for x:

Now take the positive solution, multiply it by C, and then multiply that by 5.6.

This will be the bearing of the path you should take next.  You will walk past a 4-way intersection and continue through until you reach a circular rest area. Take a rest and enjoy the view.  Count the number of sitting logs (some may be hidden in the long grass).  Record this number as E = _____  (Note: The last time Dragon counted there was 5, which means one is missing!) Continue down the opposite side of the hill that you came from, and take the path north.

At a three-way intersection where you can see a pond, stop and figure out this problem:

Make a regular polygon with "E" sides.  Use 9.7 for the length of each side.  Find the area of the polygon = ______ (Ok, so we threw a geometry problem in.)
 

The area of the polygon is your new heading.  Take this path until you come to a bridge.  Count the number of board that make up the ramp up to the bridge and record this number as K = _____.  (Don't count the little sliver of a board.)

Go across the bridge and the path will curve to the right.  When you come to a split, take the path that runs along the pond, and then come out into the clearing.  Look to your left and go to a ladder-less tower.  Look on the southeast corner of the cement base.  Find the date there.
 

Find three arithmetic means between the date and year numbers:

Date ___  ___  ___ Year

Find the common difference of this arithmetic sequence and record it as D = _____.  Now record the number of corner posts supporting the tower as H = _____, and the month number on the cement as I = _____. 

Now solve this polynomial equation by factoring:       x³ - 7x² + 15x - 9 = 0

Record your three solutions.  1 = _____  2 = _____  3 = _____

Add all three solutions and record this number as Q = ______

Now use all these numbers in this equation and solve for x:

This will be your new heading.  You will soon meet up with another trail and be heading north.  You will pass a "possible" trail going left, then a trail going to the right, and then find one to the left that you should take.  You will then come to a T.

At this point, use L, the baseball number, minus 10 as your bearing.  Take this trail until you come to a boardwalk.  As you cross it, count the number of large rectangular sheets you walk across, and record this number as J = _____ (Teacher note: some are NOT rectangles, but you'll know what to count).

From here, continue on a 340-degree bearing.  When the trail splits, take the path to the right.  Along the way, find the "number in gold" on your right and record it as Z =  _____.  You will pass one intersection, then at a "Y" head right, and then stop at the next intersection (looks like an "X") and solve this equation using numbers you have already recorded:

Y varies jointly as J and K and inversely as E. (K is the constant of variation.)
Find the appropriate combined-variation equation.
Evaluate it to find Y for the given values of J, K, E.     Y= _____

This will be your new heading.  Take this path until you come to a fence made of driftwood on your left.  Now take the path south for a while until you come to a triangle roundabout.  Stand in the center of the triangle amongst the logs.  Speaking of logs, solve the following logarithm equation:

log_Z(x² - 133x + 4717) = 7  (Note: "Z" is the base of the log.)


You should get two solutions.  One is the bearing you need and the other is the number of steps to take on that bearing.  You have to figure out which is which!

BEFORE RETRIEVING THE BOX, BE SURE NO ONE IS AROUND TO SEE YOU GET THE BOX!  DO NOT BRING ATTENTION TO YOURSELF OR THE HIDING LOCATION OF THE BOX!

You should end up at a bush with a pile of rocks at its base.  Buried under a couple of layers of rocks is the box.
But wait!  The box has a lock on it!  You need the combination to open it!  To get the combination, first multiply the following matrices.



Now use the first three A’s in the answer as your three numbers for the combination.

Please make sure you re-hide the box well, covering it with a couple layers of rocks and leaves so it is not visible from any direction. Make it look natural.  Also be sure to lock up the box and to mix up the numbers on the lock.  Thanks!

Before you set out read the waiver of responsibility and disclaimer.

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