Search by Topic

Resources tagged with Mathematical reasoning & proof similar to Tet-trouble:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 178 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof

problem icon

Perfectly Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The sums of the squares of three related numbers is also a perfect square - can you explain why?

problem icon

Air Nets

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

problem icon

Why 24?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

problem icon

AMGM

Stage: 4 Challenge Level: Challenge Level:1

Choose any two numbers. Call them a and b. Work out the arithmetic mean and the geometric mean. Which is bigger? Repeat for other pairs of numbers. What do you notice?

problem icon

Three Frogs

Stage: 4 Challenge Level: Challenge Level:1

Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .

problem icon

Sprouts Explained

Stage: 2, 3, 4 and 5

This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with. . . .

problem icon

Some Circuits in Graph or Network Theory

Stage: 4 and 5

Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

problem icon

Multiplication Square

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

problem icon

Power Quady

Stage: 4 Challenge Level: Challenge Level:1

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

problem icon

Impossible Sandwiches

Stage: 3, 4 and 5

In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.

problem icon

Chocolate Maths

Stage: 3 Challenge Level: Challenge Level:1

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

problem icon

Unit Interval

Stage: 4 and 5 Challenge Level: Challenge Level:1

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

problem icon

Yih or Luk Tsut K'i or Three Men's Morris

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

problem icon

Largest Product

Stage: 3 Challenge Level: Challenge Level:1

Which set of numbers that add to 10 have the largest product?

problem icon

To Prove or Not to Prove

Stage: 4 and 5

A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.

problem icon

The Triangle Game

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you discover whether this is a fair game?

problem icon

Whole Number Dynamics V

Stage: 4 and 5

The final of five articles which containe the proof of why the sequence introduced in article IV either reaches the fixed point 0 or the sequence enters a repeating cycle of four values.

problem icon

Whole Number Dynamics III

Stage: 4 and 5

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

problem icon

Even So

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

problem icon

Whole Number Dynamics II

Stage: 4 and 5

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

problem icon

The Pillar of Chios

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

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

problem icon

Mindreader

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

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. . . .

problem icon

Salinon

Stage: 4 Challenge Level: Challenge Level:1

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

problem icon

Always Perfect

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

problem icon

Always the Same

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

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

problem icon

A Biggy

Stage: 4 Challenge Level: Challenge Level:1

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

problem icon

Picture Story

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

problem icon

Areas and Ratios

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

problem icon

Natural Sum

Stage: 4 Challenge Level: Challenge Level:1

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

problem icon

Proximity

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

problem icon

Our Ages

Stage: 4 Challenge Level: Challenge Level:1

I am exactly n times my daughter's age. In m years I shall be exactly (n-1) times her age. In m2 years I shall be exactly (n-2) times her age. After that I shall never again be an exact multiple of. . . .

problem icon

Iffy Logic

Stage: 4 Short Challenge Level: Challenge Level:1

Can you rearrange the cards to make a series of correct mathematical statements?

problem icon

Rotating Triangle

Stage: 3 and 4 Challenge Level: Challenge Level:1

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

problem icon

Advent Calendar 2011 - Secondary

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

problem icon

Rolling Coins

Stage: 4 Challenge Level: Challenge Level:1

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .

problem icon

Power Mad!

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

problem icon

Whole Number Dynamics IV

Stage: 4 and 5

Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?

problem icon

A Knight's Journey

Stage: 4 and 5

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.

problem icon

Magic Squares II

Stage: 4 and 5

An article which gives an account of some properties of magic squares.

problem icon

The Frieze Tree

Stage: 3 and 4

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

problem icon

Long Short

Stage: 4 Challenge Level: Challenge Level:1

A quadrilateral inscribed in a unit circle has sides of lengths s1, s2, s3 and s4 where s1 ≤ s2 ≤ s3 ≤ s4. Find a quadrilateral of this type for which s1= sqrt2 and show s1 cannot. . . .

problem icon

Happy Numbers

Stage: 3 Challenge Level: Challenge Level:1

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

problem icon

Picturing Pythagorean Triples

Stage: 4 and 5

This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.

problem icon

Common Divisor

Stage: 4 Challenge Level: Challenge Level:1

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

problem icon

Whole Number Dynamics I

Stage: 4 and 5

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

problem icon

Take Three from Five

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

problem icon

Reverse to Order

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

problem icon

Logic, Truth Tables and Switching Circuits Challenge

Stage: 3, 4 and 5

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

problem icon

Angle Trisection

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

problem icon

Pythagorean Triples I

Stage: 3 and 4

The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!