Creating and manipulating expressions and formulae

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Favourite

Fibs

Age

11 to 14

Challenge level

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
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Boxed In

Age

11 to 14

Challenge level

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
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Mindreader

Age

11 to 14

Challenge level

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.
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Seven Up

Age

11 to 14

Challenge level

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?
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Quick Times

Age

11 to 14

Challenge level

Can you verify and generalise these equations?
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Please Explain

Age

11 to 14

Challenge level

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.
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Top-Heavy Pyramids

Age

11 to 14

Challenge level

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
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Favourite

How Many Miles to Go?

Age

11 to 14

Challenge level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
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Magic Sums and Products

How to build your own magic squares.
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Algebra Match

Age

11 to 16

Challenge level

A task which depends on members of the group noticing the needs of others and responding.