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Do Unto Caesar

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?

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Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

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3388

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Rod Fractions

Age 7 to 14 Challenge Level:

What fraction is the yellow rod of the orange rod? 
 


Use this picture to help you. Note that it only uses orange and yellow rods.

 

You might like to use the interactivity further down this page to help you answer the following problems:

Using as many brown and red rods as you like, but no rods of any other colours, work out what fraction the red rod is of the brown one.



Using as many red and orange rods as you like, but no rods of any other colours, work out what fraction the red rod is of the orange one.

 
 

Can you find any other pairs of rods so that the length of the shorter rod compared with the longer rod is a fraction with 1 as its numerator? 





Given an unlimited supply of any two differently coloured rods, can you find a general rule to work out what fraction the shorter rod is of the longer one?

You may like to explore this by using the pairs of colours suggested below as starting points.

Dark green and blue:

 

Pink and orange:

 

Light green and orange:

 

Why does your rule work?

Now, looking back at the different pairs of rods you have explored, can you find a way to express the longer rod as a fraction of the shorter rod?