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Resources tagged with Mathematical reasoning & proof similar to Pole Star Sudoku:

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

Age 11 to 14 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? Disappearing Square

Age 11 to 14 Challenge Level:

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . . How Many Dice?

Age 11 to 14 Challenge Level:

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. . . . Konigsberg Plus

Age 11 to 14 Challenge Level:

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. Tourism

Age 11 to 14 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. Go Forth and Generalise

Age 11 to 14

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. Iffy Logic

Age 14 to 18 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 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. . . . 9 Weights

Age 11 to 14 Challenge Level:

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

Age 11 to 18 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. . . . The Triangle Game

Age 11 to 16 Challenge Level:

Can you discover whether this is a fair game? Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate? Pattern of Islands

Age 11 to 14 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... Concrete Wheel

Age 11 to 14 Challenge Level:

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

Age 11 to 14 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? Clocked

Age 11 to 14 Challenge Level:

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours? 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. . . . Aba

Age 11 to 14 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. Convex Polygons

Age 11 to 14 Challenge Level:

Show that among the interior angles of a convex polygon there cannot be more than three acute angles. Marbles

Age 11 to 14 Challenge Level:

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades? More Marbles

Age 11 to 14 Challenge Level:

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour? Triangle Inequality

Age 11 to 14 Challenge Level:

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm. Dicing with Numbers

Age 11 to 14 Challenge Level:

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? Some Circuits in Graph or Network Theory

Age 14 to 18

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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. . . . Janine's Conjecture

Age 14 to 16 Challenge Level:

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . . Eleven

Age 11 to 14 Challenge Level:

Replace each letter with a digit to make this addition correct. Volume of a Pyramid and a Cone

Age 11 to 14

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts. Cycle It

Age 11 to 14 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. Ordered Sums

Age 14 to 16 Challenge Level:

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . . Cross-country Race

Age 11 to 14 Challenge Level:

Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places? Picture Story

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

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. . . . Ratty

Age 11 to 14 Challenge Level:

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

Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities. To Prove or Not to Prove

Age 14 to 18

A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples. Age 7 to 14

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. Unit Fractions

Age 11 to 14 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. Logic

Age 7 to 14

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

Age 11 to 14

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

Age 7 to 18

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. . . . Multiplication Square

Age 14 to 16 Challenge Level:

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

Age 14 to 16

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why! The Great Weights Puzzle

Age 14 to 16 Challenge Level:

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest? A Long Time at the Till

Age 14 to 18 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem? Advent Calendar 2011 - Secondary

Age 11 to 18 Challenge Level:

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

Age 14 to 16 Short Challenge Level:

What is the largest number of intersection points that a triangle and a quadrilateral can have?