Search by Topic

Resources tagged with Mathematical reasoning & proof similar to Weekly Problem 33 - 2011:

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

There are 94 results

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

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

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

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

Eleven

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

Replace each letter with a digit to make this addition correct.

problem icon

Is it Magic or Is it Maths?

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

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .

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

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

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

More Mathematical Mysteries

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

problem icon

Tis Unique

Stage: 3 Challenge Level: Challenge Level:1

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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

One O Five

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

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. . . .

problem icon

Dicing with Numbers

Stage: 3 Challenge Level: Challenge Level:1

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

problem icon

1 Step 2 Step

Stage: 3 Challenge Level: Challenge Level:1

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

problem icon

Konigsberg Plus

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

problem icon

Children at Large

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

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

problem icon

Go Forth and Generalise

Stage: 3

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

problem icon

9 Weights

Stage: 3 Challenge Level: Challenge Level:1

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

problem icon

Seven Squares - Group-worthy Task

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

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

problem icon

Cycle It

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

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.

problem icon

Sticky Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

problem icon

Pyramids

Stage: 3 Challenge Level: Challenge Level:1

What are the missing numbers in the pyramids?

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

What Numbers Can We Make?

Stage: 3 Challenge Level: Challenge Level:1

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

problem icon

Tourism

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

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.

problem icon

Ratty

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

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

problem icon

Königsberg

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

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?

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

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

The Triangle Game

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

Can you discover whether this is a fair game?

problem icon

Paradoxes

Stage: 2 and 3

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

problem icon

Pattern of Islands

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

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

problem icon

Online

Stage: 2 and 3 Challenge Level: Challenge Level:1

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.

problem icon

Shuffle Shriek

Stage: 3 Challenge Level: Challenge Level:1

Can you find all the 4-ball shuffles?

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

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

Cyclic Quadrilaterals

Stage: 3 Challenge Level: Challenge Level:1

What can you say about the angles on opposite vertices of any cyclic quadrilateral? Working on the building blocks will give you insights that may help you to explain what is special about them.

problem icon

Growing Ls

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

Can you fit Ls together to make larger versions of themselves?

problem icon

Con Tricks

Stage: 3

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

problem icon

Top-heavy Pyramids

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

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

problem icon

Coins on a Plate

Stage: 3 Challenge Level: Challenge Level:1

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

problem icon

A Chordingly

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

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

problem icon

More Number Pyramids

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

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

problem icon

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.

problem icon

Unit Fractions

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

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.

problem icon

Tessellating Hexagons

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

Is it true that any convex hexagon will tessellate if it has a pair of opposite sides that are equal, and three adjacent angles that add up to 360 degrees?

problem icon

Football Champs

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

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.

problem icon

How Many Dice?

Stage: 3 Challenge Level: Challenge Level:1

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

problem icon

Aba

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

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.

problem icon

Concrete Wheel

Stage: 3 Challenge Level: Challenge Level:1

A huge wheel is rolling past your window. What do you see?