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#### Resources tagged with Mathematical reasoning & proof similar to Can You Find a Perfect Number?:

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### There are 95 results

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

### Three Neighbours

##### Stage: 2 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

### What Do You Need?

##### Stage: 2 Challenge Level:

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

### Even So

##### Stage: 3 Challenge Level:

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?

### Always, Sometimes or Never? Number

##### Stage: 2 Challenge Level:

Are these statements always true, sometimes true or never true?

##### Stage: 3 Challenge Level:

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

### Square Subtraction

##### Stage: 2 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

### Elevenses

##### Stage: 3 Challenge Level:

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

### Cows and Sheep

##### Stage: 2 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

##### Stage: 3 Challenge Level:

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

### What Numbers Can We Make Now?

##### Stage: 3 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

##### Stage: 2 Challenge Level:

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

### Always the Same

##### Stage: 3 Challenge Level:

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?

### Top-heavy Pyramids

##### Stage: 3 Challenge Level:

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

### Pyramids

##### Stage: 3 Challenge Level:

What are the missing numbers in the pyramids?

### Unit Fractions

##### Stage: 3 Challenge Level:

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.

### Cycle It

##### Stage: 3 Challenge Level:

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

### Children at Large

##### Stage: 3 Challenge Level:

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

### Always, Sometimes or Never?

##### Stage: 1 and 2 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true?

### Take One Example

##### Stage: 1 and 2

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

##### Stage: 1 and 2 Challenge Level:

Who said that adding couldn't be fun?

### Tower of Hanoi

##### Stage: 3 Challenge Level:

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

### Take Three Numbers

##### Stage: 2 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

### Tri-colour

##### Stage: 3 Challenge Level:

Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?

### What Numbers Can We Make?

##### Stage: 3 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

### Aba

##### Stage: 3 Challenge Level:

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

### Advent Calendar 2011 - Secondary

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

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

### One O Five

##### Stage: 3 Challenge Level:

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

### Pattern of Islands

##### Stage: 3 Challenge Level:

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...

### Königsberg

##### Stage: 3 Challenge Level:

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

### More Number Sandwiches

##### Stage: 3 and 4 Challenge Level:

When is it impossible to make number sandwiches?

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

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

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. . . .

### 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!

### Pythagorean Triples II

##### Stage: 3 and 4

This is the second article on right-angled triangles whose edge lengths are whole numbers.

### 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.

### The Triangle Game

##### Stage: 3 and 4 Challenge Level:

Can you discover whether this is a fair game?

### More Number Pyramids

##### Stage: 3 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### 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. . . .

##### Stage: 3 and 4 Challenge Level:

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Breaking the Equation ' Empirical Argument = Proof '

##### Stage: 2, 3, 4 and 5

This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.

### Con Tricks

##### Stage: 3

Here are some examples of 'cons', and see if you can figure out where the trick is.

### Tourism

##### Stage: 3 Challenge Level:

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

### Sticky Numbers

##### Stage: 3 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

### Logic

##### Stage: 2 and 3

What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.

### Online

##### Stage: 2 and 3 Challenge Level:

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

### A Chordingly

##### Stage: 3 Challenge Level:

Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.

### Ratty

##### Stage: 3 Challenge Level:

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?

### More Mathematical Mysteries

##### Stage: 3 Challenge Level:

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

### The Genie in the Jar

##### Stage: 3 Challenge Level:

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .

### Thirty Nine, Seventy Five

##### Stage: 3 Challenge Level:

We have exactly 100 coins. There are five different values of coins. We have decided to buy a piece of computer software for 39.75. We have the correct money, not a penny more, not a penny less! Can. . . .

### Geometry and Gravity 2

##### Stage: 3, 4 and 5

This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.