Deceptively Easy

Number Theory Level 2

Give me the smallest three digit number that results the same when the digits are multiplied or added together.

Image Credit: Flickr Malka Dubrawsky


The answer is 123.

Vaibhav Kandwal by Vaibhav Kandwal , 21, India

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3 solutions

Edwin Gray
Apr 15, 2019

one should think of the smallest perfect number which is 6. Then 123 = 1 + 2 + 3 = 1 X 2 x 3.

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Ruby Syuukyoku
Nov 19, 2015

What if one wrote 000?

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That wouldn't be a 3-digit number mate!

Vaibhav Kandwal - 4 years, 11 months ago
Prakhar Dhumas
Apr 5, 2015

just have the factors of the smallest perfect no. in increasing order.

i.e. 6= 1 x 2 x 3

so the required no. is 123

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