Kirk Balk School Mathematics Department

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Maths Puzzles

Puzzle One: Efficient cutting

Challenge Level:3Challenge Level:3Challenge Level:3 Challenge

Cylinder standing on paper sheet


A cylindrical container, like the tin cans used to package some food, can be made by using two circles for the ends and a rectangle which wraps round to form the body.

To make cylinders of varying sizes, the 3 pieces can be cut from a single rectangle of flat sheet in several ways. For example:

three possible ways to cut a cylinder from A4 paper

CHALLENGE:
Use a single sheet of A4 paper and make a cylinder with the greatest possible volume.
The cylinder must be closed off by a circle at each end.
What are its dimensions?

(We will assume that the dimensions of an A4 sheet of paper are 21cm and 29.6 cm)

This puzzle is taken from the NRich Maths Website. This this website for many similar puzzles and investigations.

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Puzzle Two: A Numbered Route

Challenge Level:3Challenge Level:3 Challenge

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

10 by 10 array of random digits from 0 to 9

You may start and finish where you like, and go horizontally, vertically or diagonally but you may only pass through a number once and the line must not cross itself at any point.

If you repeat this but only go horizontally and vertically and never go diagonally, what is the highest score then?

This puzzle is taken from the NRich Maths Website. This this website for many similar puzzles and investigations.

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Puzzle Three: The Money Maze

Challenge Level:3 Challenge
Go through the maze, collecting and losing your money as you go. You may not go through any cell more than once, and can only go into a cell through a gap, for example, you may not go from 5 to 6, or from 7 to 3.

the money maze


Which route gives you the highest return? How much is it?
Which route gives you the lowest return? How much is it?

This puzzle is taken from the NRich Maths Website. This this website for many similar puzzles and investigations.

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