Mathman 8 -
The OBEZAG Letterbox
Rachel Lee, Alaina Miller, Kristina Loescher, Jamie Cooper

Students and parents of students should read my introduction to letterboxing before seeking the boxes.

These clues rely on the use of matrices to encode/decode clues.  Go to this page to learn how to do this on a free graphics calculator simulator or to do it by hand.

Clues:

1)      Before heading out on your Letterboxing adventure, decode this matrix that will tell you where your adventure begins:
 

      Go to the structure in the NW corner of  this intersection:

________________________________________________________

2)      Next count the number of boards that make up the gazebo floor and add 4.  (Do not count the boards of the outside perimeter.)  Divide this number _______by the number of circles________ that surround the gazebo. j = __________  (Round to the nearest whole number if needed.)  Find the jth term in the 5th row of Pascal's Triangle k = _______.  This number will be your compass bearing for the direction you need to head.

3)      Continue a ways until you arrive at a fun little kid’s happy place.  Count the number of normal slides _____. (Don't count the very little slide, or the pool slides seen from your location.)  Count the number of steering wheels ________.  Use these numbers to find the first 8 terms of the arithmetic sequence these numbers form:

___  ___  ___  ___  ___  ___  ___  ___ 

      t₁ = the number of slides                     t₈  = the number of steering wheels

(Note: There are fractions in the sequence.)

Add the 4 middle numbers together (t₃ to t₆ ). This number will be your new bearing.______

4)      After sliding down a slide, go to the sign in front of the park.  There are 2 kids on it.  Go north to the next park sign.  From this spot, skip in the direction of your new bearing.

5)      When you get to the next intersection, use this equation to find your new bearing:

      (q / p) / m = new bearing  _____________ (round to nearest whole number)

      q = the phone number on your left (without the hyphen)

      p = the top street sign number on your right

      m = 5 over the speed limit on the busier road by you.

6)      Go in this new direction for awhile.  View the beautiful scenery of Cedarburg and wave to all the cars as they go by. (Hint: Sing a song. It makes the time go by faster.  “Follow the parallel lines…Follow the parallel lines… Follow, Follow, Follow, Follow, Follow the parallel lines….We’re off to see the letterbox, the wonderful letter box of OBEZAG!!!”)

7)      Figure out this problem:  y varies directly as x. When y = 57600, x = 6480.  Find the constant of variation. ________ Stay on this same road until you get to an intersection where the top street sign varies directly as the bottom street sign with the same constant of variation.

8)      Next find the 3rd term of the 10th row in Pascal's triangle and multiply that by 2. _______ That will equal the angle at which you should cross the street.  Next take the 9th term of the 10th row in Pascal's triangle and multiply that by 2. ________ This is the angle you should cross the road at a second time.   (Hint:  Don’t jay walk!!)

9)      Continue down the road a short distance.  Look for a plaque that is on the first stone building you come to.  Find the last two digits of the year this building was made a Wisconsin landmark: (a)_____  Head south and cross the street.   Take a peak at the city mural.  Count how many bridges are painted on it: (b)______  Keep heading south and stop at the first restaurant on your left. (Hint: It comes right away and it smells like pepperoni.  Grab a pizza for later.)  Add up the digits in the address of the restaurant signally including the zip code: (c)_____  Continue straight and when you come across the first church on your left, stop.  Find out when the church was founded by looking at the cornerstone: (d)______ From here, glance across the street.  Find a big stone which states the year Cedarburg was founded: (e)______  (Hint: You may cross the street to get a clearer look, but come back.)  Continue down this sidewalk until you come across a T –shaped intersection.  To figure out which direction you should travel, solve this equation for the positive solution of x:

bx² – ax – d = c + e

Take the first 3 digits of the positive solution.  Multiply it by 10 (to remove the decimal) and then reverse the digits to form a new 3 digit number.  This is your new bearing: _________

10.)    Now, before you finish this exciting letterbox trip you may wish to stop and enjoy the wonderful coffee houses of Cedarburg.  (Hint: We recommend a mocha with caramel, include the whip cream.)

11.)    Next, go down the street which your bearing indicated.  When you get to the corner, look ahead.  On the front of the building should be the city zip code.  Multiply the 5 digits of the zip code together: ________  This number your new bearing.

12.)    Cross the road in the direction of your bearing, and continue on until you get to some public buildings.  Count the number of windows on the side of the Lincoln building facing the road: _____. When you arrive at the end of the road, change your direction so you head west.

13.)    Continue on this direction until you get to the first road that may be the name of a church- but it's not the name of the church it is by currently.  Take the number on top of the street sign which is located on the opposite corner from where you are standing. __________  Use this number for y in the following equation and solve for x:
 

x² - 100x - 45240 = y 

       
This will be your new bearing._______  Continue on.  Skip to the third intersection in that direction.  Stop abruptly.  (Warning: As you go check your pace!  Go only 5 mph.  Stop at the sign on your left and watch for children.  Speeding tickets are handed out often!)  At the intersection, change your bearing to 0. Head in that direction.  (Friendly advice: Peak in the sewer drains.  The Ninja Turtles may be on break.  If you feel the urge, stop and have a chat with them.  Now would be a nice time to share a slice of your pizza!) 

14.)    Continue in that direction.  (Hint:  If you need help in finding your way, listen to the “Force”.  It will lead you in the right direction.  P.S.  It is leading you north.) Stay on this path until you arrive at a nutty street (as though you couldn't tell things were getting nutty!).  Cross the street at a 90 degree angle, then continue north.

15.)    Stop at the next intersection.  Figure out this problem to find your new bearing. 

f(x) = 5x

g(x) = 63x

        Find f(g(x)) = ______.  Use the coefficient of this answer for your new bearing.

        From here skip about 31 skips, and you should reach your destination.  Sit and mediate in the middle of your final stop while graphing this lovely math equation (hint): 

y = [x]

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

(Note: The shape of the graph is also represented in one of the names of this type of function.)

The shape of this graph will tell you where your letterbox is located. Please put the letterbox back in its home, so others may come and visit it. (P.S. Its name is Bob.  Say "hi"!)

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

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