Sum of Cubes

Computer Science Level 3

How many positive integers are there such that the number is equal to the sum of the cubes of its digits?

For example $153$ is one of the numbers because $153=1^3+5^3+3^3$

The answer is 5.

3 solutions

Brock Brown
Jan 2, 2015

def valid(x):
    total = 0
    for digit in str(x):
        total += int(digit)**3
    return total == x
count = 0
for i in xrange(1, 100000):
    if valid(i):
        count += 1
print "Answer:", count

L S
Dec 16, 2014

There are 5 numbers:

$1=1^3$

$153=1^3+5^3+3^3$

$370=3^3+7^3$

$371=3^3+7^3+1^3$

$407=4^3+7^3$

Since the problem is tagged under CS, do you have a cs solution?

Mardokay Mosazghi - 6 years, 5 months ago

Here is a python solution:

count=0
for number in range(1,10000):
    sumOfCube=0
    copy=number
    while number>0:
        sumOfCube+=(number%10)**3
        number//=10
    if sumOfCube==copy:
        count+=1
print count

There cannot be a 5-digit number that satisfy the criteria because the largest sum of cube of a 5-digit number is $5*9^3=3645$

The answer is $\boxed{5}$

l s - 6 years, 5 months ago

thanks @lucy s

Mardokay Mosazghi - 6 years, 5 months ago

Hasmik Garyaka
Oct 5, 2017

Python has declarative sintax:

def sum3digits(n):
     return sum((int(x))**3 for x in map(int,str(n)))

def problem527227():
    for i in range(1000000):
        if i==sum3digits(i): print(i)

Sum of Cubes

The answer is 5.

3 solutions

0 pending reports