Numbers can be special

Computer Science Level 4

A number is said to be special if the sum of the squares of its digits on even places is equal to the sum of the squares of its digits on odd places.

For example,
$354$ is a special number, because $3^{2} + 4^{2} = 5^{2} = 25$ .
$1784$ is a special number, because $1^{2} + 8^{2} = 7^{2} + 4^{2} = 65$ .

Let $f(n)$ be a function that counts the number of special numbers less than or equal to n, and $g(n)$ be a function that finds the sum of special numbers less than or equal to $n$ . Find $g(f(f(10^{6})))$ .

The answer is 605.

2 solutions

Soumava Pal
Mar 20, 2016

>>> def special(n):
        m=n
        c=0
            p=0
        while m>0:
                d=m%10
                c+=1
                if c%2==1: p+=d*d 
                else: p-=d*d
                m/=10
         if p==0: return 1
         return 0

>>> def f(n):
         c=0
         for i in range(1,n+1):
            if special(i)==1:
                c+=1
         return c

>>> def g(n):
         c=0
         for i in range(1,n+1):
            if special(i)==1:
                c+=i
         return c

>>> g(f(f(10**6)))
605
>>>

Python:

def isspecial(n):
    a = str(n)
    if sum(int(x)**2 for x in a[::2])==sum(int(x)**2 for x in a[1::2]):
        return True
    else:
        return False

def f(n):
    return sum(1 for i in range(1,n+1) if isspecial(i))
def g(n):
    return sum(i for i in range(1,n+1) if isspecial(i))

A Former Brilliant Member - 5 years, 1 month ago

Agnishom Chattopadhyay
Mar 22, 2016

I feel a little functional today. This might be slower though, but tight cute code.

Python 3

def specialQ(n):
    n = str(n)
    odd, even = 0,0
    for i in range(0,len(n)):
        if i%2:
            odd += int(n[i])**2
        else:
            even += int(n[i])**2
    return odd == even

f = lambda n: len(list(filter(specialQ,range(1,n+1))))
g = lambda n: sum(filter(specialQ,range(1,n+1)))

Finally, run

1 2	`>>> g(f(f(1000000))) 605`

4 lines for everything.

Python 3, 196 characters (204 bytes)

special=lambda n: sum((-1)**i*int(n[i])**2 for i in range(len(n)))==0
f=lambda n: sum(special(str(i)) for i in range(n+1))
g=lambda n: sum(i*special(str(i)) for i in range(n+1))
print(g(f(f(10**6))))

A bit slower than your code though.

Prasun Biswas - 5 years, 2 months ago

Yeah, this is cool too

Agnishom Chattopadhyay - 5 years, 2 months ago

Numbers can be special

The answer is 605.

2 solutions

Python 3, 196 characters (204 bytes)

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