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Click on a button below to try a similar puzzle with different sized jugs.

Can you work out how to do each puzzle in the minimum number of moves?

Can you find any general rules which apply to this kind of challenge?

Investigations Home

Brain Food,

Wednesday, February 19, 2014

"You're a cook in a restaurant in a quaint country where clocks are outlawed. You have a four minute hourglass, a seven minute hourglass, and a pot of boiling water. A regular customer orders a nine-minute egg, and you know this person to be extremely picky and will not like it if you overcook or undercook the egg, even by a few seconds. What is the least amount of time it will take to prepare the egg, and how will you do it?"

SimÃ©on Denis Poisson, A long time ago

Sunday, June 10, 2018

"Two friends who have an eight-quart jug of water wish to share it equally. They also have two empty jars, one holding five quarts, the other three. How can they each measure exactly four quarts of water?

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A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.

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Colour the sweet wrappers so that no two are the same. A multi-level activity designed to encourage a systematic strategy for finding all of the different permutations.

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You will need to be quick on the draw to shoot all of the numbers except the square numbers. So far this activity has been accessed 57806 times and 473 people have earned a Transum Trophy for completing it.

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