This is an extension to yesterday’s question. We are still looking at how positive whole numbers can be expressed as the sums of square numbers.

This time we are looking at how some numbers can be expressed as different sums of squares. Again, we are only allowed a maximum of four squares and a minimum of, obviously, just one.

For example, 9 can be simply expressed as 3

^{2}, but it can also be made from 2

^{2}+ 2

^{2}+ 1

^{2}. The number 11 can only equal 3

^{2}+ 1

^{2}+ 1

^{2}; there are no other sums of squares that can equal 11 unless we use more than four of them.

So, our question this time is to find those numbers between 20 and 30 inclusive that can be expressed as the sums of squares in only one unique way and using a maximum of four squares.

**Feel free to comment, ask questions and even check your answer in the comments box below powered by Disqus.**

**If you enjoy using this website then please consider making a donation - every little helps :-)**

**You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.**

**Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..**

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.

## No comments:

## Post a comment