**Python Puzzles**

There are 5 people, each with a different height. They all stand in a straight line, and you stand directly in front of them looking at them.

How many different arrangements of those 5 people are possible that would have exactly 3 people visible to you?

There are 35 different arrangements.

```
[(1, 2, 5, 3, 4), (1, 2, 5, 4, 3), (1, 3, 2, 5, 4), (1, 3, 5, 2, 4), (1, 3, 5, 4, 2),
(1, 4, 2, 3, 5), (1, 4, 2, 5, 3), (1, 4, 3, 2, 5), (1, 4, 3, 5, 2), (1, 4, 5, 2, 3),
(1, 4, 5, 3, 2), (2, 1, 3, 5, 4), (2, 1, 4, 3, 5), (2, 1, 4, 5, 3), (2, 3, 1, 5, 4),
(2, 3, 5, 1, 4), (2, 3, 5, 4, 1), (2, 4, 1, 3, 5), (2, 4, 1, 5, 3), (2, 4, 3, 1, 5),
(2, 4, 3, 5, 1), (2, 4, 5, 1, 3), (2, 4, 5, 3, 1), (3, 1, 2, 4, 5), (3, 1, 4, 2, 5),
(3, 1, 4, 5, 2), (3, 2, 1, 4, 5), (3, 2, 4, 1, 5), (3, 2, 4, 5, 1), (3, 4, 1, 2, 5),
(3, 4, 1, 5, 2), (3, 4, 2, 1, 5), (3, 4, 2, 5, 1), (3, 4, 5, 1, 2), (3, 4, 5, 2, 1)]
The number of different arrangements is 35
```

# import the itertools module to create permutations of the list [1, 2, 3, 4, 5] import itertools # create a list of all possible permutations of the list [1, 2, 3, 4, 5] permutations = list(itertools.permutations([1, 2, 3, 4, 5])) my_list = [] # loop through each permutation of the list for my_tuple in permutations: i = 0 visible = 1 #initialize the largest value in the tuple to the first value largest_value = my_tuple[0] # loop through each element of the tuple while i < len(my_tuple) - 1: # if the current element is larger than the largest value so far, increment visible and update largest_value if largest_value < my_tuple[i+1]: visible = visible + 1 largest_value = my_tuple[i+1] i = i + 1 # if there are 3 visible towers, add the tuple to my_list if visible == 3: my_list.append(my_tuple) # print the list of tuples with 3 visible towers and the number of different arrangements print(my_list) print('The number of different arrangements is', len(my_list))