Cute Numbers

Date: 08/29/2003 at 11:47:37
From: Paul Bates
Subject: Cute Numbers

I have found two definitions of a cute number. They are

1. If a square can be cut into n squares of at the most two 
different sizes, then n is called a cute number. For example, 4 and 
10 are cute numbers.

and

2. A number with only 4 factors is a cute number. For example 6 
{1,2,3,6}

Which is the correct definition? The second one seams more 
interesting, as the first definition includes all numbers over 5.

Date: 08/29/2003 at 12:11:42
From: Doctor Peterson
Subject: Re: Cute Numbers

Hi, Paul.

I'm inclined to agree with you, up to a point. I believe that the 
problem in our archives about "cute numbers" is not referring to a 
generally accepted term, but just temporarily defining "cute" for the 
sake of the problem. As you point out, once you have solved the 
problem you realize that "cute" hardly means anything, so there is no 
point in retaining the definition.

The other definition is more interesting, and even more fitting; but 
I have never heard it before, and find it in only one page when I 
search. So I suspect that this, too, is just one person's temporary 
definition, and not something commonly agreed upon. It just happens 
to be more worth keeping than the other.

So my answer is: neither is really "the correct definition"! (You 
left out that possibility.) It is an undefined term, as far as 
mathematicians in general are concerned.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/