One Line Problem

Number Theory Level 1

Find 3 integers whose product (of all 3 integers) is equal to their sum (of all 3 integers).

Image credit: Wikipedia Mike R
1 , 2 , 3 0 , 1 , 2 2 , 3 , 4 0 , 1 , 3

View wiki
Vishnu Ps by Vishnu Ps , 26, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

10 solutions

Mohit Asswani
Sep 14, 2014

1 2 3=6
1+2+3=6

6 Helpful 0 Interesting 0 Brilliant 0 Confused

But the picture suggests that you should find 3 integers that, separately, have the same product and sum e.g. 2+2=2x2

Luke Middleton - 6 years, 8 months ago
Dladla Arthur
Sep 18, 2014

1 2 3 = 6

1+2+3 = 6

therefore 1,2,3 are the required three integers.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

1x2x3 = 6; 1 + 2+ 3 = 6, so the sum of 1, 2, and 3 is identical with their product. 6 is therefore a "perfect number."

John M Lewis - 6 years, 8 months ago
Claire Meng
Oct 11, 2014

1+2+3 = 6

Then 2x3= 6 6x1=6

1 Helpful 0 Interesting 0 Brilliant 0 Confused

These kind of numbers, the product of whose divisors is equal to their sum, are so awesome, that they are given the title of perfect numbers! The first perfect number is 6, since 1 + 2 + 3 = 1 × 2 × 3 1+2+3 = 1\times 2 \times 3 and hence the answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mini Prasad
Sep 18, 2014

1+2+3=1 X 2 X 3

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Advaita Nitturkar
Sep 18, 2014

1 times 2 times 3 =6 1 plus 2 plus 3=6

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Don Robbins
Sep 18, 2014

1+2+3=6. And 1x2x3=6

1 Helpful 0 Interesting 0 Brilliant 0 Confused

1 2 3=1+2+3=6

0 Helpful 0 Interesting 0 Brilliant 0 Confused

1 × 2 × 3 = 6 1 \times 2 \times 3 =6
1 + 2 + 3 = 6 1 + 2 + 3 =6

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sophie Crane
Sep 27, 2014

Multiple choice was really not the way to go with this one. You should have asked for their product/sum as an input.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...