List

Spreadsheets

Excel investigation: More Beads
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Excel investigation: more beads

A heap of beads was shared out by a professional bead sharer. Use the information given to find out how many beads there were at the start.
Excel investigation: Number Pyramids
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Excel investigation: number pyramids

Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.
Excel investigation: Happy Numbers
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Excel investigation: Happy numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

Excel Investigation: Planks
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Excel investigation: planks

I have an unlimited supply of planks, of lengths 7 and 9 units. Putting planks end to end, what total lengths can be achieved? Use Excel to investigate.
Excel Investigation: Difference Tuples
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Excel investigation: difference tuples

Use an Excel spreadsheet to investigate differences between four numbers. Which set of start numbers give the longest run before becoming 0 0 0 0?
Plates of Biscuits
problem

Plates of biscuits

Age
7 to 11
Challenge level
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Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
Multiples Grid
problem

Multiples grid

Age
7 to 11
Challenge level
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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

problem

Factor-multiple chains

Age
7 to 11
Challenge level
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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Substitution Cipher
problem

Substitution cipher

Age
11 to 14
Challenge level
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Find the frequency distribution for ordinary English, and use it to help you crack the code.

Take Ten Sticks
problem

Take ten sticks

Age
11 to 16
Challenge level
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Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
What's the weather like?
problem

What's the weather like?

Age
11 to 14
Challenge level
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With access to weather station data, what interesting questions can you investigate?

Sending a Parcel
problem

Sending a parcel

Age
11 to 14
Challenge level
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What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Time of birth
problem

Time of birth

Age
11 to 14
Challenge level
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A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?
Litov's Mean Value Theorem
problem

Litov's mean value theorem

Age
11 to 14
Challenge level
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Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Cola can
problem

Cola can

Age
11 to 14
Challenge level
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An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Under the Ribbon
problem

Under the ribbon

Age
14 to 16
Challenge level
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A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?
Euler's Squares
problem

Euler's squares

Age
14 to 16
Challenge level
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Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Odd Differences
problem

Odd differences

Age
14 to 16
Challenge level
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The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Tree tops
problem

Tree tops

Age
14 to 16
Challenge level
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Can you make sense of information about trees in order to maximise the profits of a forestry company?

Training schedule
problem

Training schedule

Age
14 to 16
Challenge level
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The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Pythagoras’ Comma
problem

Pythagoras' comma

Age
14 to 16
Challenge level
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Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

Minus One Two Three
problem

Minus one two three

Age
14 to 16
Challenge level
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Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?
Negative 3 to the power of negative 3.
problem

Negative powers

Age
14 to 18
Challenge level
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What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

The Fire-fighter's Car Keys
problem

The fire-fighter's car keys

Age
14 to 16
Challenge level
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A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.
The Legacy
problem

The legacy

Age
14 to 16
Challenge level
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Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Zeller's Birthday
problem

Zeller's birthday

Age
14 to 16
Challenge level
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What day of the week were you born on? Do you know? Here's a way to find out.
Peaches in General
problem

Peaches in general

Age
14 to 16
Challenge level
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It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.
There's always One isn't there
problem

There's always one isn't there

Age
14 to 16
Challenge level
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Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
Dating made Easier
problem

Dating made easier

Age
14 to 16
Challenge level
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If a sum invested gains 10% each year how long before it has doubled its value?

problem

Funnel

Age
14 to 16
Challenge level
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A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

Succession in Randomia
problem

Succession in Randomia

Age
16 to 18
Challenge level
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By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

Stirling work
problem

Stirling work

Age
16 to 18
Challenge level
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See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Any win for tennis?
problem

Any win for tennis?

Age
16 to 18
Challenge level
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What are your chances of winning a game of tennis?
Time to evolve 2
problem

Time to evolve 2

Age
16 to 18
Challenge level
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How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?