### Upsetting Pitagoras

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

### Rudolff's Problem

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

### Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

# Coffee

##### Age 14 to 16Challenge Level

Many students used trial and improvement techniques to show that to blend the coffee then 4kg of Mocha, 2 kg of Kenyan and 5 kg of Brazilian are needed if the conditions are to be satisfied. These included students from Maidstone Girls Grammar School; West Flegg Middle School; Madras College; Strabane Grammar School; Trinity Academy, Edinburgh; Our Lady's Grammar School, Newry; Clevedon Community School, Somerset and ACS Barker, Singapore.

Joshua of Russell Lower Scholl, Ampthill, Bedfordshire arrived at his solution which his father called trial and error techniques. There is an easier and quicker way submitted by Lyndsay of Mount school, York, which is represented below:

M + K + B = 11 (11 kg in all)
13M + 14K + 17B = 165 (cost is £165)
so 13 ( 11 - K - B) + 14K + 17B = 165
143 - 13K - 13B + 14K + 17B = 165
K + 4B = 22

Since B > K, the only whole numbers that fit are B = 5 and K = 2
So the answer is 5 kg Brazilian, 2 kg Kenyan and 4 Kg Mocha.