This is not a cache designed to be solved in five minutes from the driver’s seat.
The posted coordinates are only the STARTING POINT.
The final cache location is hidden behind five mathematical challenges.
You may need:
• Calculator
• Paper and pencil
• Patience
• Careful arithmetic
There are FIVE PARTS.
Each part produces information needed for the next stage.
Do not round intermediate answers unless specifically instructed.
PART I — POLYNOMIAL
Consider the function:
f(x) = x⊃3; − 6x⊃2; + 11x − 6
TASK
-
Find all real roots of f(x) = 0.
-
Arrange the roots from smallest to largest.
-
Call the roots A, B, and C.
-
Calculate:
M = (A + B)⊃2; + (B + C)⊃2; + (C + A)⊃2;
-
Calculate the number of possible permutations of the three roots.
-
Multiply M by that number.
Your result is PART I.
PART II — MUSIC / PITCH CLASSES
You are given the following notes:
C — E♭ — F♯ — A — B♭ — D — E
Use this chromatic pitch-class system:
C = 0
C♯ / D♭ = 1
D = 2
D♯ / E♭ = 3
E = 4
F = 5
F♯ / G♭ = 6
G = 7
G♯ / A♭ = 8
A = 9
A♯ / B♭ = 10
B = 11
TASK
-
Convert each note to its pitch-class number.
-
Calculate the interval between each pair of adjacent notes using modulo 12.
-
Reduce each interval to its interval class.
-
Add all interval classes.
-
Count the number of distinct pitch classes.
-
Add that number to your interval-class total.
Your result is PART II.
PART III — SPECIAL RELATIVITY
A spacecraft travels directly away from Earth at a constant velocity.
The spacecraft’s onboard clock measures:
12.000 seconds
Earth-based observers measure the same interval as:
15.000 seconds
Use:
t = γ × τ
and
γ = 1 / √(1 − v⊃2;/c⊃2;)
where:
τ = proper time
t = time measured by the outside observer
v = spacecraft velocity
c = speed of light
TASK
-
Calculate γ.
-
Solve for v/c.
-
Express v/c as a percentage.
-
Round to the nearest whole percent.
-
Multiply that percentage by the number of letters in:
SERAPHINE
Your result is PART III.
PART IV — ASTRONOMY
A star has an annual parallax of:
p = 0.010 arcseconds
Its apparent magnitude is:
m = 7.50
Its absolute magnitude is:
M = 2.50
Use the distance-modulus equation:
m − M = 5 × log₁₀(d) − 5
where d is the distance in parsecs.
Also use:
d = 1 / p
and:
1 parsec = 3.26156 light-years
TASK
-
Determine the distance in parsecs using the distance modulus.
-
Determine the distance in parsecs using parallax.
-
Confirm that both methods agree.
-
Convert the distance to light-years.
-
Take only the integer portion.
Your result is PART IV.
PART V — FINAL COORDINATE
You should now have four answers.
For reference, label them:
A = PART I
B = PART II
C = PART III
D = PART IV
Do not use a coordinate converter yet.
The following calculations transform your four answers into the final coordinate.
NORTH
Calculate:
N1 = A ÷ 10 − 1
The NORTH degrees are:
45°
The NORTH minutes are:
N1
For the NORTH seconds, calculate:
N3 = ((C − A) ÷ 7.5) + ((B − 15) ÷ 30) + 0.000373333333333333
Round N3 to six decimal places.
WEST
The WEST degrees are:
87°
Calculate:
W1 = D ÷ 10 − 1
This is the WEST minutes.
For the WEST seconds, calculate:
W2 = ((C − B) ÷ 9.55) + ((A − B) ÷ 100) + 0.100414333333333
Round W2 to six decimal places.
Your coordinate should now be written as:
NORTH:
45° [N1]′ [N3]″ N
WEST:
87° [W1]′ [W2]″ W
Use the following conversion when checking your work:
Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600
Your final coordinate should be accurate to 7 decimal places.
🔎 FINAL CHECK
Before traveling to the final location:
-
Verify every answer from Parts I–IV.
-
Verify your Part V calculations.
-
Convert your DMS coordinate to decimal degrees.
-
Make sure your NORTH and WEST coordinates agree with the required precision.
-
If they do not, go back and check your arithmetic.
The posted coordinates are NOT the final cache location.
Do not attempt to solve the puzzle while driving.
Once you have your final coordinates, enter them into your GPS.
Good luck!
FINAL FORMAT
N XX° XX.XXXXXX′
W XXX° XX.XXXXXX′