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Building Tetrahedra

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

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?


Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Fruity Totals

Age 7 to 16
Challenge Level

Fruity Totals printable sheet
Fruity Totals printable sheet - extra fruity grids

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).

This activity featured in an NRICH student webinar in November 2021.

You may also be interested in the other problems in our Is there a better way? Feature.