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%% Cell type:markdown id: tags:
# Python course 2023 - Exercises B
%% Cell type:markdown id: tags:
## Part1 - control structures
%% Cell type:markdown id: tags:
---
1.1) Write a script for guessing numbers!
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```
a = 3
b = input("Zahl eingeben: ")
print(a + int(b))
```
%% Output
Zahl eingeben: 5
8
%% Cell type:markdown id: tags:
---
1.2) Add tips (smaller/larger) during the guessing process!
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```
```
%% Cell type:markdown id: tags:
---
BONUS TASK
1.3) Add additional tips (e.g. much smaller/ much larger) during the guessing process!
%% Cell type:code id: tags:
```
```
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# Repetition functions
%% Cell type:markdown id: tags:
---
![image.png](data:image/png;base64,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)
%% Cell type:code id: tags:
```
```
%% Cell type:markdown id: tags:
---
![image.png](data:image/png;base64,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)
%% Cell type:code id: tags:
```
```
%% Cell type:markdown id: tags:
---
![image.png](data:image/png;base64,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)
%% Cell type:code id: tags:
```
```
%% Cell type:markdown id: tags:
---
![image.png](data:image/png;base64,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)
%% Cell type:code id: tags:
```
```
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