Swap It and See

 Which do you think is the larger?:              

The Problems:


Choose any two numbers that add to 1.

Be as clever or simple as you like. 

Now square one of these numbers, and add the result to the other number.

Write down your answer.

Swap the numbers around – squaring the second number and adding the result to the first number.

What do you think of that, then? Try it with two other numbers that add up to 1. Go clever.


Now think of two numbers that add to 10 – any two numbers, mind.

Square the first number, and add the result to 10 times the second number.

Repeat this with the two numbers swapped around. 

Try a few other, let’s-make-really-sure-of-this sorts of numbers (e.g. 2.8457239 and 7.1542761), and check that the rule really works… 


See if you can generalise from this last ‘trick’, and make up another rule about two numbers adding up to some total.

Can you think of a way to explain what’s happening here?

The diagram below might help with the very first result – for numbers adding to 1.

Open the File as a Word Document


Send site mail to admin@1000problems.org  or personal comments direct to sdakeyne@psc.ac.uk with questions or comments about this web site.
Last modified: June 18, 2007