Creating and manipulating expressions and formulae
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problemMagic W
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
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problemConsecutive Squares
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
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problemJanine's Conjecture
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. Does this always work? Can you prove or disprove this conjecture?
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problemHand Swap
My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?
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problemNever Prime
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
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problemArchimedes and Numerical Roots
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
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problemTriangles Within Squares
Can you find a rule which relates triangular numbers to square numbers?
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problemWalk the Plank
A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?