What to design for the exam from Arduino?

Question

Arduino

Good day to all!
It's very simple: I'm a college student in my second year in a major related to IT, and I should have a session soon.
I can write programs for Arduino and can solder almost anything. At the same time, I have a good command of C.
So far, our educational process includes how to use Microsoft Office.
On January 20, we have an exam in physics, but they told me that if I bring some kind of device based on MK, they will automatically pass me a test.
I have been working on three difficult projects for a year now and I will not be able to finish a single one, purely physically, before January 20th.
So I wanted you to suggest something that I can whip up with an Arduino and impress the examiners in turn.
PS
I'm not asking you to give me ready-made ideas or paint everything with pieces of code and circuit boards.
I want to do all the work myself. I'm asking for a purely idea, in the spirit of: "Make a robot driving along a drawn line."
PPS
A short list of what I have:
Arduino UNO, LCD (16x2), sensor shield, motion sensor PIR, two 9g servos, three DC motors, one stepper, one RGB and a bunch of regular LEDs also resistors, transistors, etc. (if the radio market is not far away and I can buy small things, but there is almost no money).

Answer 1

Measuring device. Choose one of the experiments in mechanics or electrodynamics and make a visual aid with automatic measurement and calculations.

Answer 2

And if you automate the collection of data from any of the laboratory? Let's say one that has a large enough stream of incoming data, and now you have to perform calculations on just a few samples.
PS I now remember the laboratory workshop in physics with difficulty, but there were definitely experiments with pendulums, in which it was necessary to time the repetition of the passage of the pendulum through control points with great accuracy - your device would cope with this or similar things just fine.

Answer 3

A robot that will find its own way out of a complex maze.

Answer 4

Automatic curtain control.
Voice control of the water faucet/door.
A robot drawing with a marker on a large sheet (A0).

Answer 5

LED matrix
example

Answer 6

If memory serves, we at the institute wrote software for microcontrollers that takes a matrix and a vector as input and multiplies a given matrix by a given vector. The trick, however, was to write all this in assembler and interact correctly with the terminal. How do you like this problem?

Answer 7

And what about a plotter, with the possibility of relief processing, or let's say that it could repeat the movements of the operator, such a "brush"

Answer 8

If you find a book: "To help the radio amateur. Issue 82", then it contains a description of the textbook "Dynamic model of pn transition", which was developed by M. Gershanovich, Yu. Morozov, M. Muralev. You can assemble the same one, but on new components, or show the work of other semiconductors.
An example of that scheme can be found here: otvet.mail.ru/question/82779305