### Upsetting Pitagoras

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

### Lunar Leaper

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

### Seriesly

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

# Odd One Out

##### Stage: 5 Short Challenge Level:

The interactivity below has been programmed to generate random numbers according to 6 different and well defined random processes. You can generate as many of these sets of data as you like by pressing the 'New Data' button.

HOWEVER: for each process there is a deliberately placed bad item of data (whose location varies each time you make new numbers) which breaks the pattern shown by the other numbers.

By searching for structure and suspicious numbers, can you work out which is the likely odd one out in each case? (full screen mode)
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Use the scroll bars to input your choices of the bad rows and press 'Check' to see if you are correct: if you are then the whole column will turn red; otherwise the computer will ignore you. Good luck!

Discuss: Can you ever be certain that you are correct in your assessment of the odd ones out? Can you give a statistical justification as to why your guesses are likely to be correct?