This Sunday, the 2nd season of Take Off kicks off! With new participants and three exciting challenges! But what about you – would you be able to solve this challenge?

What is this challenge about?

In this challenge, the participants must find out the height of the tower at Vianden Castle.

You enter a deserted room - the instructions for the challenge are posted at the entrance. There is a plan of the castle on the floor. In one of the rooms, two Playmobil figures are standing; this room is the only one that has been measured. There is also a 3D model of the Vianden watchtower on the plan, which is exactly 1m40 high.

The participants have a tape measure at their disposal, as well as a pen, paper and calculator.  

Do you want to do the challenge?

What is the real height of the tower?


Here is all the data you need:

  • The height of the model tower is 1400 mm
  • The dimensions of the room on the plan are (W=218 mm) x (L=356 mm)
  • The width of the room in which the candidates are located: 5.45 m
  • The length of the room in which they are located: 8.9 m

The model tower and the map are on the same scale, but on which scale? 

Infobox

Solution

The participants have the size of the model tower in front of them: 1400 mm. Now the task is to find out the scale of the model tower in order to know how much larger the real tower is. To calculate a scale, you must determine the relationship between the size shown on the plan and the actual size (in the real world).

The participants must therefore take a measurement from the room and compare it with the room shown on the plan. The Playmobil figures on the plan indicate which room they are in. 

The real length or width of the room must therefore be divided by the corresponding length on the plan:

Real width = 5.45 m; width on the plan = 218 mm.

5450/218=25: the scale is therefore 1:25, which means that the tower is 25 times larger in reality than in the model.

1,4*25=35

Solution: The real tower is 35 meters high

Here you can see how the candidates solved this challenge:
(You will have to wait until the 5th of January until the episode is officially released)

What is the scientific background to this challenge?

Scaling of drafts

In architecture, and generally when generating maps, blueprints are often drawn to scale, and the rule of three is used to convert between the scale lengths and the actual sizes.

Example: The plan of Vianden Castle uses a scale of 1:25, which means that 1 m on the plan corresponds to 25 m in the real world.

 

A few impressions from the first episode

How do you get an egg out of a cylinder without tilting the cylinder? (Eggs do not float in water!)

Author: Diane Bertel

Editors: Lucie Zeches (FNR), Joseph Rodesch (FNR)

Photos: Emmanuel Claude

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