Author of this question: Steffi Knorn, Fachgebiet Regelungstechnik, Technische Universität Berlin, Germany
Dolls are a classic Christmas gift, so it’s no surprise that part of Santa’s workshop is dedicated to making dolls and their dresses. Every morning, the two teams—the doll makers and the dress makers—meet to check how many dolls and dresses are already made, and then they plan what to do for the rest of the day. Each team has a different way of working:
- The doll makers count the dolls in the workshop and decide as an initial plan for that day to make the same number of dolls they see in the workshop. Their argument is that if there are that many dolls from yesterday, they can do as many today. However, if they see dresses lying around without dolls, they get distracted by the beautiful dresses and for each dress, they will make one less doll.
- The dress makers count the dolls in the workshop and make as many dresses as there are dolls, independently of whether they are dressed or not. So if there are 5 dolls, they’ll make 5 dresses.
Then, at the end of the day, the packing elves come in and check how many dolls can be dressed (to be dressed, each doll needs one dress of course). They take half the dolls that can be dressed and the corresponding dresses, dress the dolls, and then take them away to wrap them up. If the number of dolls that can be dressed is odd, they take just a bit less than half.
Santa believes that this system is perfect, so he can leave the workshop unattended. The first day he visits the workshop in the morning, he sees three dolls and one dress and the elves just starting their day. What will happen then?
a. 🎄🧸🧝 The elves will produce only dolls after a while.
b. 🎄👗🧝 The elves will produce only dresses after a while.
c. 🎄⏹️😴 The elves will stop working already on day two.
d. 🎄⚖️✅ Everything will work out very well. The elves will produce a steady amount of dolls and dresses every day.
e. 🎄🔄📊 Everything will work out very well. The elves will produce dolls and dresses every day with some periodic fluctuations over time.
f. 📈👗🧸 The elves will even increase their productivity and keep producing more and more dolls with dresses.