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problem

Sugary Diversion

11 to 14

Weekly Problem 48 - 2008
An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?

problem

Mean Square

11 to 14

Can you fill this square so that the number in the middle of each line is the mean of the two numbers on either side of it?

problem

Building Up

11 to 14

In the diagram, the number in each box is obtained by adding the two immediately below. What is the number in the top box?

problem

Pebbles

7 to 11

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

problem

Favourite

More Twisting and Turning

11 to 16

It would be nice to have a strategy for disentangling any tangled ropes...

problem

Favourite

Tetra Perp

16 to 18

Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.