I just need to check all 900 cases

Logic Level 4

What is the sum of all 3-digit positive integers for which the multiplication of the sum of its digits and the product of its digits equals to the number itself?

The answer is 279.

3 solutions

Sharky Kesa
Jun 13, 2015

I made a simple Python code for this problem.

for a in range(1,10):
    for b in range(0,10):
        for c in range(0,10):
            if 100*a + 10*b + c == a*b*c*(a+b+c):
                print 100*a + 10*b + c

This gives us the values 135 and 144. 135+144=279.

i did the same, but is there a way to find it without a computer ?

Ashwath Srikanthan - 6 years ago

Yes there is.I used the other method.Took Me 10 mins but was worth it

Kaustubh Miglani - 4 years, 11 months ago

How did you do it?

Zainul Niaz - 3 years, 8 months ago

How do you insert a program/code file in the solution box? @Sharky Kesa

Samarpit Swain - 5 years, 10 months ago

Tap space a couple of times (4 should do it)

Sharky Kesa - 5 years, 10 months ago

Three backticks ( ` )at the beginning and end of the code will produce the following result :

code

Vishnu Bhagyanath - 5 years, 10 months ago

Satyen Nabar
Jun 13, 2015

These are called Sum-Product numbers explained here

Tom Engelsman
Sep 21, 2020

There are only two such numbers: $135$ and $144.$

I just need to check all 900 cases

The answer is 279.

3 solutions

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