Special Palindromes

Computer Science Level 2

A palindrome is a positive integer that reads the same forwards and backwards; e.g., 101 and 2552 are both palindromes.

What is the smallest x x for which x x and x + 2016 x+2016 are both palindromes?


The answer is 646.

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Khang Nguyen Thanh by Khang Nguyen Thanh , 27, Vietnam

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5 solutions 

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def ispalindrome(n):
    if n==int(str(n)[::-1]):
        return True
    else:
        return False
a=1
while a>0:
    if ispalindrome(a) and ispalindrome(a+2016):
        print(a)
        break
    else:
        a+=1

4 Helpful 1 Interesting 0 Brilliant 0 Confused

Nice! The function definition for ispalindrome(n) is really elegant (+1 for this) , although you can make it even more concise as, 

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def ispalindrome(n):
    return n==int(str(n)[::-1])

Prasun Biswas - 5 years, 5 months ago

+1 for [::-1]. What a pythonic way of reversing string!

Hun-Min Park - 5 years, 5 months ago
Sonveer Yadav
Dec 18, 2015

for (2016+x) to be palindrome, no should be of the form 2aa2, where 'a' represent the digits.

2aa2 = 2016 + x

2000+100a+10a+2 = 2016+x

2002+110a = 2016+x

x = 2014 - 110a

now putting a=1,2,3... we get palindrome on a=6 i.e x=646

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Dec 17, 2015

by trial and error.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Bill Bell
Dec 16, 2015 
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def palindrome(n):
    result=0
    while n>0:
        result=10*result+n%10
        n=n/10
    return result 

x=1
while True:
    if x==palindrome(x) and x+2016==palindrome(x+2016):
        print x
        break
    x+=1

2 Helpful 1 Interesting 0 Brilliant 0 Confused
Faisal Basha
Dec 16, 2015

/(2662 - 2016 = 646 )/

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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