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Guillotine

11 to 14

Weekly Problem 9 - 2006
What fraction of the area of the rectangle is shaded?

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Next-door numbers

5 to 7

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

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Tetra inequalities

16 to 18

Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?

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Favourite

Cubes within cubes revisited

11 to 14

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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The clockmaker's birthday cake

7 to 11

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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Hot pursuit

11 to 14

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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Multiple magic

11 to 14

Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

problem

Dilution series calculator

14 to 16

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

problem

Favourite

Impossibilities

11 to 14

Just because a problem is impossible doesn't mean it's difficult...

problem

Favourite

Three neighbours

7 to 14

Take three consecutive numbers and add them together. What do you notice?