These are the random problems I have taken from project eular, along with the answers and the python code for it,
for outer in range(100,1000) :
for inner in range(100,1000):
if outer*inner > number and str(outer*inner) == str(outer*inner)[::-1]:
number = inner*outer
print number
The answer will be 906609. This is an easy question you just multiplying 3 digits number and check is whether it is a palindrome and get the biggest number.
2. The prime factors of 13195 are 5, 7, 13 and 29.
divisor = 2
while number > divisor:
if number % devisor == 0:
number = number/divisor
else:
divisor = devisor + 1
return number
The answer will be 6857, the program takes a number input from the key board and prints the highest prime factor of the entered number. The program is similar to the long division we do manually. If a prime divides a number, it is reduced to the number/division,
Then the time taken for the program to execute will law.
3. The sum of the squares of the first ten natural numbers is,
for outer in range(1,101):
for inner in range(outer+1,101):
difference = difference + inner*outer
print difference*2
This is an interesting question, we can get the sum of the squares and square of sums very easily and get the difference, but it will not be time effective. So i have used (a+b)^2 - (a^2 + b^2) = 2ab in this program.
Answer will be 25164150.
4. Find the greatest product of five consecutive digits in the 1000-digit number.
index = 0
max_sum = 0
while index < len(number)-4:
total = 1
for i in range(5):
total = total*int(number[index+i])
if total > max_sum:
max_sum = total
index = index + 1
print max_sum
This is a huge number, in the program it take it as the input and and iterate over 5 places to get the product of 5 consecutive numbers and stores it if it the maximum number that has been found so far. Answer will be 40824.
That is the final problem i have discussed today, wishing to be back from more interesting problems.
Thank You.
1. A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 
99.
99.
Find the largest palindrome made from the product of two 3-digit numbers.
number = 0for outer in range(100,1000) :
for inner in range(100,1000):
if outer*inner > number and str(outer*inner) == str(outer*inner)[::-1]:
number = inner*outer
print number
The answer will be 906609. This is an easy question you just multiplying 3 digits number and check is whether it is a palindrome and get the biggest number.
2. The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
number = input()divisor = 2
while number > divisor:
if number % devisor == 0:
number = number/divisor
else:
divisor = devisor + 1
return number
The answer will be 6857, the program takes a number input from the key board and prints the highest prime factor of the entered number. The program is similar to the long division we do manually. If a prime divides a number, it is reduced to the number/division,
Then the time taken for the program to execute will law.
3. The sum of the squares of the first ten natural numbers is,
12 + 22 + ... + 102 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)2 = 552 = 3025
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 
385 = 2640.
385 = 2640.
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum
difference = 0for outer in range(1,101):
for inner in range(outer+1,101):
difference = difference + inner*outer
print difference*2
This is an interesting question, we can get the sum of the squares and square of sums very easily and get the difference, but it will not be time effective. So i have used (a+b)^2 - (a^2 + b^2) = 2ab in this program.
Answer will be 25164150.
4. Find the greatest product of five consecutive digits in the 1000-digit number.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
number = input()
max_sum = 0
while index < len(number)-4:
total = 1
for i in range(5):
total = total*int(number[index+i])
if total > max_sum:
max_sum = total
index = index + 1
print max_sum
This is a huge number, in the program it take it as the input and and iterate over 5 places to get the product of 5 consecutive numbers and stores it if it the maximum number that has been found so far. Answer will be 40824.
That is the final problem i have discussed today, wishing to be back from more interesting problems.
Thank You.
0 comments:
Post a Comment