Electronic – Gernerate random circuits to measure with multimeter

I want to create a game, where players have to analyse a circuit in order to solve a puzzle. The players see 6 measuring points A to F and have a multimeter/continuity tester. They also have a few different schematics. They now have to find out which schematic is representing the circuit they have in front of them. The Circuits have random shorts or diodes between the measuring points and can look like this:

The thing now is, that I want to be able to generate random circuits with the help of a microcontroller. I'd like to have something like an Arduino simulating different circuits. They don't actually have to work, they just have to look like one of the circuits to a continuity tester.

If I could bruteforce my way through it, I could use 15 relays (one for each connection AB, AC, AD, AE, AF, BC, BD, …) to switch on and off a short and 30 more relays for 15 diodes in one direction and 15 diodes in the other direction. But my PCB isn't big enough for that 😉

Is there any other way to simulate shorts and diodes to a continuity tester using a microcontroller? I'd even be happy with something like "The microcontroller senses which points get measured and outputs something the multimeter/continuity tester can interpret". As I said, the circuits don't actually have to work.

Edit: I don't want to simulate the continuity tester. I want the players to learn how to use the "real thing".