{"id":511,"date":"2024-12-09T08:00:00","date_gmt":"2024-12-09T07:00:00","guid":{"rendered":"https:\/\/control-advent.com\/?p=511"},"modified":"2025-11-28T19:04:55","modified_gmt":"2025-11-28T18:04:55","slug":"09-chevis-challenge-bikes-bandages-and-balance","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=511","title":{"rendered":"09 – Mercurina\u2019s Challenge: Bikes and Magical Bandages"},"content":{"rendered":"\n

Author of this question:<\/strong> Steffi Knorn, Fachgebiet Regelungstechnik<\/em>, <\/em>Technische Universit\u00e4t Berlin, Germany<\/p>\n\n\n\n

The elves in Santa’s workshop are way behind on making gifts, so the head supervisor elf has given the order: <<Roll up your sleeves and get to work!>> Each elf in charge of a different section now has to boost productivity to reach their targets.<\/p>\n\n\n\n

Elf Mercurina, who leads the section for making bicycles, gets the goal of making 18 bikes in the next five days. She knows that the higher she and her team roll up their sleeves, the faster they can work. For example, everybody rolling sleeves up one level will make the team produce one bike per day, rolling up two levels will lead to two bikes per day, and so on.

However, rolling sleeves higher comes with risks. When sleeves are rolled up, the elves\u2019 arms are more exposed, which can lead to more scratches and scrapes. With the extra speed and movement, their arms are also more likely to bump into things, increasing the chance of injuries. So, this means the number of injuries increase quadratically with the level of rolled-up sleeves. For example, rolling sleeves up to level five results in about 25 injuries per day for the whole team, while level two only leads to about four injuries per day for the whole team.

Each injury needs a magical bandage, which works well but can\u2019t be reused and is expensive. So, Mercurina wants to keep injuries – and the need for bandages – as low as possible.

What\u2019s the best plan for Mercurina to make the team meet the bike goal while also minimizing injuries and saving on bandages?<\/p>\n\n\n

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a. \ud83d\udeb4\u200d\u2642\ufe0f\ud83d\udcaa\ud83c\udf89 Have all elves roll up their sleeves to six and get going and produce as many bikes as possible. That’s the whole point of rolling up sleeves anyway! And any extra bikes can be used for the elves themselves to have some fun in the workshop the last day.<\/p>\n\n\n\n

b. \ud83d\udee0\ufe0f\ud83c\udfaf\ud83d\ude0c Have all elves roll up their sleeves to six and get going. As soon as the target number of bikes is reached, roll down the sleeves to zero and relax.<\/p>\n\n\n\n

c. \ud83d\udcc6\ud83e\udd1d\ud83d\udeb2 Have all elves roll up their sleeves to three for two days and roll up to four for three days. The order of the days with sleeves rolled up to three or four does not matter.<\/p>\n\n\n\n

d. \u23f3\ud83d\udcc9\ud83d\udeb4\u200d\u2642\ufe0fHave all elves roll up their sleeves to four each day until the second last and then reduce to roll up sleeves to two the last day.<\/p>\n\n\n\n

e. \ud83d\udd22\u2728\u2696\ufe0f Have all elves roll up their sleeves to three because this is half way and seems like a good compromise. And three is a magic number, isn’t it?<\/p>\n\n\n\n

f. \ud83e\udde5\ud83d\udee1\ufe0f\ud83c\udf43 Have all elves roll up their sleeves to one to make sure the number of injuries is minimal.<\/p>\n\n\n

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