Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# There's Always One Isn't There

## You may also like

### DOTS Division

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Systematic working and recording of results help a lot here.

Conjectures are important, and should be encouraged, but along with a challenge to really explain why any claim might be true generally.

We are so familiar with numbers and what they do, or what we believe they do, that the challenge to account rigorously for the familiar can seem pedantic. Hopefully the problem expressed in this form will give students the pleasure of discerning real structure.

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.