Puzzle for 2nd International Day of Mathematics 2021 – Immune in no time!

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And yet again there is a major wave of the contagious snowpox disease infection in Elf Town. However, this year a new form of snowpox has appeared and has now arrived at the North Pole. Therefore, today, the Elf Council has carried out rapid testing throughout Elf Town. In the evening, Mayor Elsbeth convenes the entire Elf Council to present the results and further measures.

At the meeting, Taidula, the chief medical officer of Elf Town, first describes the problem: "All together, 85 of the 100,000 elves in Elf Town, today tested positive for the new snowpox." Elf Fredi gets quite hysterical: "Oh no, not again! How many elves do you reckon will get infected this time?" Taidula replies: "This new form is already known from other regions of the world. We know that a newly infected elf is ill for three days. On average, before the snowpox becomes visible, an infected elf infects two other elves on the 2nd day of the illness. As a rule, the elves are cured on the 4th day after infection and can no longer infect anyone else.”


Elsbeth tries to reassure the elves: "Look, we already have a vaccine. We have arranged for enough staff and vaccine so that we can start vaccinating tomorrow and on any given day we will vaccinate 7,500 healthy elves."

Taidula adds: "There is therefore reason for hope: Elves healed from snowpox, and vaccinated elves are immune to the disease. This means that they can no longer themselves get infected with the new snowpox and can no longer infect any other elves. In order to break the wave of infection and quickly prevent the occurrence of many serious cases, we need to get more than half of all elves immune to new snowpox."

By the end of how many days will more than half of the 100,000 elves be immune?

[Note: An elf who is vaccinated or recovers from sickness is already immune at the end of the same day. The 1st day is the "today", the day of the Elf Council gathering. The vaccinations therefore start on the 2nd day. For the estimation, assume that the 85 elves are all on the 1st day of their illness.]

This puzzle was created from:

„Mathe im Advent”–Team
Mathe im Leben gemeinnützige GmbH

This puzzle was translated from:

An English family living in Berlin, the son Ben and the parents Fiona & Carl Isaac. 

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