85 Follower problem

Number Theory Level 4

Determine the sum of all three digit number N N such that N N is divisible by 11 and N 11 \dfrac{N}{11} is equal to sum of the square of the digit of N N .

Bonus :- Find for such 4 digit numbers


The answer is 1353.

Department 8 by Department 8 , 27, Israel

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2 solutions

Sahil Goyat
Jul 4, 2020 
1
 
sum(i for i in range(100,1000) if i%11==0 and int(i/11)==sum([int(j)**2 for j in str(i)]))

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Razing Thunder
Jul 3, 2020 
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def sums(int):
    a=  (int )% 10
    b=(int%100)//10
    c=int//100
    return a**2 + b**2 + c**2
#print(sum(123))
x=[]
for i in range(100,1000):
    a=int(i)
    if int(i)%11 == 0 :
        if (i/11) == sums(a):
            x.append(i)
print(sum(x))

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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