def problem_4():
print("\nVous avez sélectionné le problème suivant :")
print("-----------------------------------")
print("Quel est le plus grand palindrome que l'on peut obtenir en multipliant un nombre de x chiffres avec un nombre de y chiffres ?")
print("===================================\n")
digit1 = utilities.check_input("Veuillez entrer le premier nombre de chiffres : ")
digit2 = utilities.check_input("Veuillez entrer le deuxième nombre de chiffres : ")
# Get the greatest number in the range of the digit (example : if digit = 3, max = 999)
greatest1 = utilities.greatest_number(digit1)
greatest2 = utilities.greatest_number(digit2)
palindrome = 0
# Multiplication till a palindrome is found
for number1 in range(greatest1, -1, -1):
for number2 in range(greatest2, -1, -1):
resultat = number1*number2
# Check if it's a palindrome
if(utilities.is_palindrome(resultat)):
if(resultat > palindrome):
palindrome = resultat
print("Le nombre suivant est un palindrome : {}".format(palindrome))
def main():
n = 0
for i in range(100, 1000):
for j in range(i, 1000):
sum = i * j
if utilities.is_palindrome(sum) and sum > n:
n = sum
return n
def test_palindrome(self):
self.assertTrue(is_palindrome('kayak'))
self.assertFalse(is_palindrome('not a palindrome'))
# A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers
# is 9009 = 91 × 99.
# Find the largest palindrome made from the product of two 3-digit numbers.
from utilities import is_palindrome
products = []
for x in range(100, 1000):
for y in range(100, 1000):
products.append(x * y)
products.sort()
products = reversed(products)
for product in products:
if is_palindrome(product):
print(product)
exit(0)
from utilities import is_palindrome
palindromes = [(x*y, x, y)
for x in range(1000)
for y in range(1000)
if is_palindrome(x*y)]
print sorted(palindromes)
# The decimal number, 585 = 1001001001 (binary), is palindromic in both bases.
#
# Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.
#
# (Please note that the palindromic number, in either base, may not include leading zeros.)
from utilities import is_palindrome, to_binary_string
cumulative_sum = 0
for i in range(1000000):
if is_palindrome(i):
if is_palindrome(to_binary_string(i)):
cumulative_sum += i
print(cumulative_sum)
#
# Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
#
# How many Lychrel numbers are there below ten-thousand?
#
# NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
from utilities import is_palindrome
num_lychrel = 0
def reverse_int(num: int) -> int:
str_num = str(num)
return int(str_num[::-1])
for i in range(1, 10000):
candidate = i
lychrel = True
for j in range(50):
candidate = candidate + reverse_int(candidate)
if is_palindrome(candidate):
# This is not a Lychrel number
lychrel = False
break
if lychrel:
num_lychrel += 1
print(num_lychrel)