UNIVERSITY OF
TUPPERWARE IN THE
WOODS
Department of Mathematics
This description is best viewed in a web browser on a laptop or desktop.
Requirements for a minor in Mathematics
In order to receive a minor in mathematics, a student must pass four courses: MATH-127, MATH-228, MATH-241, and MATH-373. In order to receive a minor with Honors, they must pass an additional, online-only course, MATH-608.
Syllabus
This is a hybrid puzzle/multicache with four physical stages and a bonus puzzle-only stage. To get the coordinates for each physical stage, you must pass a one-question final exam. At the first three stages, you will find a digit. Use those digits, in the order of the course curriculum, to open a padlock that secures the container at the final stage. I recommend solving all of the puzzles first and then making a single trip to collect the digits and log the final. There is no need to visit the virtual waypoint.
Office hours
Instructors will hold office hours virtually, using the Certitude video conferencing platform. The coordinates for every physical stage are verifiable via Certitude. If a student solves the bonus stage and enters the number into Certitude, they will receive Honors credit (hints for each physical stage).
Teaching assistants
Unfortunately, the math department's graduate students are too busy doing their own research, so no teaching assistants are available. The only hide hints that are available are via office hours, as described above.
Graduation
Upon graduation, please reset the lock combination to 000.
Curriculum
MATH-127 Concepts of Mathematics
Every positive number can be written as a sum of square numbers. Lagrange's four-square theorem says that no more than four square numbers are needed, but you won't need that cool fact to pass this class.
Define the sum of square roots function \(SSR(n)\) as follows:
- Write \(n\) as a sum of square numbers.
- Take the square root of each of those square numbers.
- Add the square roots together.
For instance, \(21 = 4^2 + 2^2 + 1^2\), so \(SSR(21) = 4+2+1 = 7\). Some numbers can be written as the sum of squares in more than one way. For instance, \(65 = 8^2 + 1^1 = 7^2 + 4^2\). To resolve any ambiguity, always use the largest square numbers possible: \(SSR(65) = 8+1\) (this is a greedy algorithm).
Stage 1 is at N 37° 2\(A.BCD\) W 121° 5\(E.FGH\).
\(ABCD = SSR(8567347)\).
\(EFGH = SSR(68220946)\).
You may take your final exam here.
MATH-228 Discrete Mathematics
Let \(f(n)\) be defined as follows: \(f(n) = \begin{cases} n/2 &\text{if } n \text{ is even},\\ 3n+1 & \text{if } n \text{ is odd} \end{cases}\)
Let the Collatz sequence of a positive number \(n\) be the result of applying \(f\) repeatedly. For example, the Collatz sequence of 7 is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. Once a sequence reaches 1, it enters a cycle: 1, 4, 2, 1, ... The Collatz conjecture states that the Collatz sequence of every positive number eventually contains the number 1. This conjecture is one of the most famous unsolved problems in mathematics. It has been shown to be true for all numbers up to \(2^{68}\). The total stopping time of \(n\) is the number of steps until the Collatz sequence of \(n\) reaches 1. (Since the Collatz sequence contains numbers, and total stopping time counts steps, the total stopping time of a number is the length of its Collatz sequence - 1.) The total stopping time of 7 is 16.
Stage 2 is at N 37° 2\(A.BCD\) W 121° 58.\(EFG\).
\(AB\) is the total stopping time of 130.
\(CD\) is the total stopping time of 361.
\(EFG\) is the total stopping time of 80097.
You may take your final exam here.
MATH-241 Matrix Algebra
Stage 3 is at N 37° 2\(A.BCD\) W 121° 5\(E.FGH\). \(\begin{bmatrix} A \\ B \\ C \\ D \\ E \\ F \\ G \\ H \\ \end{bmatrix} \begin{bmatrix} A & B & C & D & E & F & G & H \end{bmatrix} = \begin{bmatrix} 4 & 16 & 6 & 10 & 16 & 6 & 18 & 8 \\ 16 & 64 & 24 & 40 & 64 & 24 & 72 & 32 \\ 6 & 24 & 9 & 15 & 24 & 9 & 27 & 12 \\ 10 & 40 & 15 & 25 & 40 & 15 & 45 & 20 \\ 16 & 64 & 24 & 40 & 64 & 24 & 72 & 32 \\ 6 & 24 & 9 & 15 & 24 & 9 & 27 & 12 \\ 18 & 72 & 27 & 45 & 72 & 27 & 81 & 36 \\ 8 & 32 & 12 & 20 & 32 & 12 & 36 & 16 \end{bmatrix} \)
You may take your final exam here.
MATH-373 Algebraic Structures
Recall that a group is a set along with an operation defined on elements of that set. A group \(G\) is cyclic if it contains an element \(g\) such that every other element of the group may be obtained by repeatedly applying the group operation to \(g\). \(|G|\) is the number of elements in \(G\), called the order of \(G\). If \(G\) is a cyclic group and \(a \in G\), \(\langle a \rangle\) is the cyclic subgroup of \(G\) generated by \(a\).
Concretely, \(\mathbb{Z}/n\mathbb{Z}\) is the cyclic group consisting of the integers \(\{0, 1, 2, ... n-1\}\) and the operation of addition modulo \(n\).
Stage 4 is at N 37° 2\(A.BCD\) W 121° 5\(E.FGH\).
\(ABCD = |\langle 6995 \rangle| \textrm{ where } G = \mathbb{Z}/14940\mathbb{Z}\).
\(EFGH = |\langle 6735 \rangle| \textrm{ where } G = \mathbb{Z}/25227\mathbb{Z}\).
You may take your final exam here.
MATH-608 Elliptic Curves
Passing this exam is extra credit. It is not required in order to log the cache. What is the \(x\) coordinate of \((5, 34) + (6, 19)\) over the elliptic curve
\(y^2 = x^3 + 3x + b \mod 127\)? The answer is a two-digit number.
You may take your final exam here.
Honor roll
Congratulations to the class of 2025, the recipients of the graduation gifts:
- StadsAlv
- chrisfawcett1
- yoyo ken
- cachbefound
- Cats4us
Updates
2025-06-13:
- Fixed puzzle for stage 4, which gave coordinates to a prior location
- Removed final coordinates from bonus stage Certitude
- Corrected some 122° to 121°
2025-06-15: updated Certitude coordinates for the bonus (virtual-only) stage from bogus coords to the parking waypoint