How Many People Are Visible

Python Puzzles

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Here is a puzzle from the book Probability – A Beginner’s Guide To Permutations And Combinations: The Classic Equations, Better Explained – Scott Hartshorn

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.

# -*- coding: utf-8 -*-
"""
Created on Sun Jan 10 21:42:01 2021

@author: smpet
"""

#creates the permutations
import itertools
permutations = list(itertools.permutations([1, 2, 3, 4, 5]))

#use below for testing specific tuples
#permutations = []
#permutations.append((4,1,2,3,5))
#permutations.append((1,2,3,4,5))
#print(permutations)

my_list = []

#Uncomment the print statements to follow the logic
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 largest_value < my_tuple[i+1]:        
    
            visible = visible + 1
            largest_value = my_tuple[i+1]
            
        i = i + 1
               
    if visible == 3: my_list.append(my_tuple)

print(my_list) 
print('The number of different arrangements is', len(my_list))