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Resources tagged with Mathematical reasoning & proof similar to Pattern of Islands:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof 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... 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? Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18 Challenge Level:

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information. 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? Not Necessarily in That Order

Age 11 to 14 Challenge Level:

Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation? Flight of the Flibbins

Age 11 to 14 Challenge Level:

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . . 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? 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? Eleven

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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. 1 Step 2 Step

Age 11 to 14 Challenge Level:

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? 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. 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? 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? 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. Iffy Logic

Age 14 to 18 Challenge Level:

Can you rearrange the cards to make a series of correct mathematical statements? 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. 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. Age 7 to 14 Challenge Level:

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed? Pyramids

Age 11 to 14 Challenge Level:

What are the missing numbers in the pyramids? Always the Same

Age 11 to 14 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? 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. . . . 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? 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. 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. 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? Age 11 to 14 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. . . . 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. . . . Proofs with Pictures

Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities. For What?

Age 14 to 16 Challenge Level:

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares. 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. . . . 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. Concrete Wheel

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

Which hexagons tessellate? 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. . . . 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. Con Tricks

Age 11 to 14

Here are some examples of 'cons', and see if you can figure out where the trick is. 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. 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. Mod 3

Age 14 to 16 Challenge Level:

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3. Unit Interval

Age 14 to 18 Challenge Level:

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

Age 14 to 18 Challenge Level:

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . . A Chordingly

Age 11 to 14 Challenge Level:

Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle. 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? 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. . . . Take Three from Five

Age 14 to 16 Challenge Level:

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? 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.  