A computer science problem by Paola Ramírez

Computer Science Level 3

How many 4-digit perfect squares A B C D ‾ \overline{ABCD} are there such that A B ‾ − C D ‾ \overline{AB}-\overline{CD} is also a perfect square?


The answer is 11.

Paola Ramírez by Paola Ramírez , 24, Mexico

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2 solutions

Mehdi K.
May 26, 2016 
1
 
sum(1 for ele in [i ** 2 for i in range(34, 100)] if ele // 100 - (ele % 100) in [i ** 2 for i in range(10)])

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Christopher Boo
May 21, 2016

Brute force solution by searching every 4 digit number and mark those that satisfies the property. 

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import math

def perfect(x):
    return math.floor(math.sqrt(x)) * math.floor(math.sqrt(x)) == x

ans = 0

for x in range(1000,10000):
    y = x / 100 - x % 100
    if perfect(x) and y >= 0 and perfect(y):
        ans += 1

print ans

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