- #1

Mark44

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## Main Question or Discussion Point

Not long ago, a member posted a problem in the Homework section, concerned with determining which of the five-digit permutations of 4, 5, 6, 8, and 9 were divisible by 8.

I first thought about writing some C code to figure this out, but when I discovered that Python has some functions that would make this problem a lot easier, I abandoned my attempt using C. The permutations() and combinations() functions in the

I don't know much Python, so I used this problem as an exercise in becoming more knowledgeable with this language. If you have any comments on my code, feel free.

Here's the solution I came up with. BTW, my program reports that the are 20 permutations that are divisible by 8, and it lists them. There are several commented-out print statements that I used for debugging purposes. I left them in place, but commented-out, instead of removing them.

I first thought about writing some C code to figure this out, but when I discovered that Python has some functions that would make this problem a lot easier, I abandoned my attempt using C. The permutations() and combinations() functions in the

**itertools**module, are very useful in this problem.I don't know much Python, so I used this problem as an exercise in becoming more knowledgeable with this language. If you have any comments on my code, feel free.

Here's the solution I came up with. BTW, my program reports that the are 20 permutations that are divisible by 8, and it lists them. There are several commented-out print statements that I used for debugging purposes. I left them in place, but commented-out, instead of removing them.

Python:

```
# plates.py
# Find all permutions of 4, 5, 6, 8, and 9 that are divisible by 8.
# I'm using license plates with five numeric digits as an analogy here.
# Algorithm:
# Construct all possible permutations of the set (4, 5, 6, 8, 9}.
# For each permutation tuple, construct in integer whose digits are generated from the given tuple.
# Strip off the two highest digits of the integer, leaving a three-digit integer.
# If the three-digit integer is divisible by 8, the five-digit number it came from is also divisible by 8.
# Display each of the five-digit numbers that are divisible by 8, together with how many there are.
import sys
import itertools
digit_set = ['4', '5', '6', '8', '9']
TotalCount = 0 # Count of all plates
Count8 = 0 # Count of plates with numbers that are divisible by 8
NumPlate = 0 # An individual license plate, as an integer
Last_three = 0
# Make a collection of plates with the five digits in the list above.
plates = itertools.permutations(digit_set, 5)
# Iterate through each item in the plates collection.
for plate in plates:
TotalCount = TotalCount + 1
#print('Plate', plate)
NumPlate = 0
# A plate is a tuple of characters (actually, strings of length 1).
# Construct a number out of the digit characters in each tuple.
for ltr in plate:
#print("Letter: ", ltr)
NumPlate = 10 * NumPlate + int(ltr)
#print('Number plate: ', NumPlate)
# Strip off the first two digits.
# If the last three digits of an integer are divisible by 8, the integer is divisible by 8.
# E.g., 1008 is divisible by 8, but 1009 is not.
Last_three = NumPlate % 1000
#print('Stripped digits: ', Last_three)
if Last_three % 8 == 0:
print('Last three digits: ', Last_three)
print('Plate number: ', NumPlate)
Count8 = Count8 + 1
else:
continue
print('Done')
print('Count of all permutations', TotalCount)
print('Count of permutations divisible by 8: ', Count8)
```