Mathman 11 -
The Rainbow Powder Box
Jacob Feutz, Cory Bergmann, Matthew Kurtz, Sarah Pastorek

 Terrain: Involves a lot of hiking and fairly steep hills. Difficulty: Depends on your math ability.  For help with sequences click here. Time: Varies - depends on your ability to follow directions. Placed by: The Dragon (Mathman) and his Honors Advanced Algebra students of 2003-04 Location: The WI State Forest near Hartford, WI County: Washington County Materials needed: Compass, Calculator, Writing Utensil, Inking pens

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

Park on the street close to the entrance of the bike trail on Franklin Drive just south of HWY 60.  Stand facing the signs and count the number of signs at the beginning of the trail.

If t1 = 1 and t3 = the number of signs, find the S8, the sum of the first eight terms of this arithmetic series.

S8=A______

Walk down the trail.  Enjoy the prairie all around you. Stop at the first sewer manhole you come across. Take a bearing of A degrees. (Note: Don't stand on the manhole as the metal will affect the compass!)  Find the three digit number on the dog bathroom in that direction. Return to the manhole and proceed as you were along the trail.

Find the ninth term of this geometric sequence, then round it to the nearest whole number.

t1= __  [number on dog bathroom]

tn= .9 tn-1

t12= B (rounded to the nearest whole number)_______

At the intersection with the four-colored pole (look off the trail to the left a bit), stand in the center of the intersection and take a bearing of B degrees and continue on that trail. Count the number of screw holes (including those with screws in them, but not the nail) on the top of the first bench you meet. Then, proceed on the trail until you come to a road. Count the number of orange stripes on one side of the barricade you come to (partial stripes included).

t1=__     [number of stripes]        t2=__     [number of holes]

tn= tn-1 + tn-2

Find the 5th term and subtract 6 to get C = ______
Find the 3rd term and subtract 16 to get D = ______

At the metal 'No Parking' sign take a bearing of C degrees and proceed down that trail.   Proceed to the "three sided island", but be careful where you stand!  Watch out for flowers!  Take a bearing of D degrees and proceed down that trail. Along the trail you will find a map with the trail distances on it. Add them all up for a single number to find the value of E = ______.

At the intersection with a short trail on your left which leads to a black "path", walk on a bearing of E degrees. Count the number of stripes in the middle of the black "path" and let this value be N = ____. (Note: Look hard, they are faded and covered a bit.)  Then go back to the trail original trail..  Take the Nth root of the 12th term of the Fibonacci number sequence times 5N minus 5N to get F=______.

Continue on the trail you were on to the next intersection (on the right).  There are a number of trails here.  Continue your hike on the trail that heads on a bearing of F degrees. Before you come to a major turn in the path, an information sign tells you about the local inhabitants. What is the name of the third inhabitant pictured on the sign?

 __ __ __ __ __   __ __ __ __ __ __ __ __ __ __  1  2  3  4  5    6  7  8  9 10 11 12 13 14 15

Follow that trail to a set of stairs and count them as you climb up.  I
f t1 = 8 and t3 = the number of stair steps, find the t39, the thirty-ninth term of this arithmetic sequence.

t39 = G = _____

At the top of the stairs head on a bearing of G degrees. As you proceed along that trail count the number of logs across the trail (only those put there on purpose). Stop counting once you reach the next bench.  Let the number of logs equal n.  Use this to find the value of H using the formula below:

At the next intersection take a bearing of H degrees and continue along that trail. When you come to a four way intersection continue walking straight ahead.  Proceed along that trail and head left at the first intersection, followed by a right at the next intersection. At the top of this hill there will be a very obvious 'landmark'. At the base of this landmark is a rock.  Fill in the first four words on the rock in the spaces below:

 __ __ __ __ __ __  __ __ __ __ 16 17 18 19 20 21  22 23 24 25 __ __ __ __ __ __ __ __ __ __ __  __ __ __ __ __ 26 27 28 29 30 31 32 33 34 35 36  37 38 39 40 41

Now get to the 'climax' of this area and count the number of 'progressions' to the 'climax'.

t3= 50.8

t5= __  [number of 'progressions']

Find the common difference constant in this arithmetic sequence and multiply it by 10.  This will give you the value of R = ______.

When you get to the climax look for the compass and fill in the blanks below:

Now use the numbers above to decode this message:

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

42 03 90 26 5  59 33 70 00 78 9  88 80 28 32 57 47 20 19 95

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

74 14 42 46 65 61 6  38 90 89 22 40 1  38 64 4  15 33 91 99

__ __ __ __ __ __ __ __ __ __ __ __ __,__ __ __ __ __ __ __

29 10 17 31 59 58 49 48 90 90 2  95 62 89 74 03 6  89 66 13

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

81 01 1  6  18 70 35 45 60 53 11 95 29 19 95 86 2  54 42 91

X  __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

X  90 71 66 57 47 89 70 00 90 71 77 72 38 39 56 36 44 18 41

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

34 95 1  69 12 17 57 32 42 40 9  10 62 36 87 45 35 30 36 85

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __:”__

21 65 95 37 22 53 33 35 16 26 90 95 22 46 89 38 64 00 41  27

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __(__ __ __

68 64 48 15 20 17 90 1  86 14 5  9  2  57 27 71 18 38 01 78

__ __ __ __)!__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

11 16 59 88)!94 4  14 95 26 34 89 73 71 66 51 60 85 36 71 33

__ __ __ __ __ __ __ __!”__ __ __ __ __ __ __ __ __ __ __ __

13 29 02 14 56 31 46 47  1  74 62 94 27 29 02 7  10 20 95 86

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

40 27 7  45 80 3  5  71 66 12 19 90 38 41 89 86 23 54 77 53

__ __ __ __ __ __  X.__ __ __ __ __ __ __ __ __ __,__ __ __ __

89 33 20 41 42 38 X  43 36 65 93 47 23 37 62 17 01 1  22 4  28

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

1  66 19 46 57 89 94 83 72 28 26 70 32 19 73 38 66 89 51 80

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

14 1  74 00 95 92 97 2  50 87 37 49 13 59 58 99 4  14 94 90

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

15 17 10 1  22 00 92 38 02 84 1  35 44 17 1  91 9  01 71 95

__ __ __ __ __ __ __ __.__ __ __ __ __ __ __ __ __ __ __ __

70 40 30 94 56 44 74 89 73 26 66 61 48 73 45 70 46 02 52 38

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

66 37 89 74 69 31 79 03 39 1  22 4  5  59 34 90 73 26 66 18

__ __ __,__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

62 54 22 42 66 33 95 74 68 6  2  3  01 64 74 43 45 86 89 74

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

29 73 70 51 19 73 91 66 90 75 36 19 1  22 68 92 46 70 87 28

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __.__

27 69 81 01 61 62 54 94 62 12 3  90 38 15 73 68 51 88 94 59

__ __ __ __ __ __ __ __,__ __ __ __ __ __ __ __ __ __ __ __

2  1  22 81 88 39 83 73 89 71 90 43 12 47 64 70 32 1  73 71

__ __ __ __ __ __ __ __ __ __ __ __ __ __,__ __ __ __ __ __

66 48 15 00 63 35 91 52 34 01 44 90 17 92 73 91 66 57 46 4

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

93 33 38 94 95 97 99 1  32 1  33 22 46 21 38 45 80 51 89 95

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __.__ __ __ __

74 53 42 65 94 14 71 90 1  86 85 89 91 98 03 60 90 49 38 61

__ __ __ __ __, __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

1  70 69 21 85  70 29 65 47 42 83 02 84 13 71 18 12 33 86 00

__ __ __ __. __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

86 79 76 96  42 68 37 98 00 4  36 89 74 20 54 69 45 91 01 47

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

9  57 47 37 70 75 49 47 54 40 33 17 90 77 35 44 94 89 86 53

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __. __ __

30 00 23 6  97 33 60 20 03 26 01 1  70 46 55 14 90 89  73 91

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

66 64 62 82 77 90 2  57 19 64 86 87 95 73 91 66 94 46 03 80

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __.

51 37 89 74 68 42 48 94 29 38 90 1  22 9  33 89 5  4  81

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