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Overturning Fracsum

Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7

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Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

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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?

Fruity Totals

Age 7 to 16 Challenge Level:
In the interactivity below, each fruit has a value between 1 and 15 inclusive.  
The sum of the values of the fruit in each row and column is shown.
Can you work out the value of each individual fruit?

Once you have had a go, you might like to try a harder level. There are five levels to choose from, and you can access them through the Settings menu by clicking on the purple 'cog' in the top right-hand corner. Don't worry if you get stuck on one of the higher levels; you can always click on a question mark to reveal the hidden total.

We would love to hear about the strategies you use to solve each grid.  You could send us a screen shot, or copy the code that appears in the Settings menu, along with an explanation of how you deduced the values.

You may like to explore Different Deductions (for younger students) or What's it Worth? (for older students).