P.E.4: Largest Palindrome Number

Computer Science Level 2

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.


The answer is 906609.

Arvind Srinivasan by Arvind Srinivasan , 26, India

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3 solutions

Brock Brown
Jan 4, 2015 
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def palindrome(x):
    return str(x) == str(x)[::-1]
biggest = 0
for a in xrange(100,1000):
    for b in xrange(100,1000):
        if palindrome(a*b):
            if a*b > biggest:
                biggest = a*b
print "Answer:", biggest

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Since, we are just interested in largest number, you could have safely searched for a , b a, b in range say 900 , 999 900,999 . This would decrease execution time.

Rushikesh Jogdand - 5 years ago
Swapnil Bhargava
Sep 22, 2014

Here's my C++ code 

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#include<iostream>
#include<cstdio>
#include<cmath>
#define llimit 100
#define ulimit 999
using namespace std;
bool checkPalindrome(long long int n)
{
    int i;
    if(n/100000)//6 digits
    {
        for(i=1;i<=3;i++)
        {
            if(((n%(long long int)pow(10,i))/(long long int)pow(10,i-1))==((n%(long long int)pow(10,7-i))/(long long int)pow(10,7-i-1)))
                continue;
            else 
                return false;
        }
    }
    else//5 digits
    {
        for(i=1;i<=2;i++)
        {
            if(((n%(long long int)pow(10,i))/(long long int)pow(10,i-1))==((n%(long long int)pow(10,6-i))/(long long int)pow(10,6-i-1)))
                continue;
            else
                return false;
        }
    }
    return true;
}
int main()
{
    long long int i,j,num,mnum=-1;
    for(i=ulimit;i>=llimit;i--)
    {
        for(j=ulimit;j>=llimit;j--)
        {
            num=i*j;
            if(checkPalindrome(num))
            {
                if(num>mnum)
                    mnum=num;
            }
        }
    }
    printf("%lld",mnum);
    return 0;
}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Arvind Srinivasan
Sep 19, 2014

My python code is as follows: 

# -*- coding: utf-8 -*-
"""
Euler Problem #4:
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."""
for i in range(99,1000):
    largest = None
    for j in range(999, 0, -1): # decreasing from 999
        if j * 999 < largest: # if True, impossible for higher product
            break 
        for k in range(999, i-1, -1): # decrease from 999 and exclude i-1
            product = k*j
            if str(product) == str(product)[::-1]:#[::-1] reverses the string
                if product > largest:
                    largest = product
    print " The largest palindrome made from the product of two 3-digit numbers is: "
    print largest
    break

Hope this helps!

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Isn't this problem from Project Euler?

Edward Jiang - 6 years, 8 months ago

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