Search by Topic

Resources tagged with Mathematical reasoning & proof similar to Score:

Filter by: Content type:
Age range:
Challenge level:

There are 163 results

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

Age 11 to 14 Challenge Level:

What are the missing numbers in the pyramids? Even So

Age 11 to 14 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? Eleven

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

Choose any three by three square of dates on a calendar page... More Mathematical Mysteries

Age 11 to 14 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. . . . Never Prime

Age 14 to 16 Challenge Level:

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime. Number Rules - OK

Age 14 to 16 Challenge Level:

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number... 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... Impossible Sandwiches

Age 11 to 18

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. 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? 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. 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? Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 16 Challenge Level:

When is it impossible to make number sandwiches? Age 11 to 18 Challenge Level:

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

Age 14 to 18 Challenge Level:

Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence. Elevenses

Age 11 to 14 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? Iffy Logic

Age 14 to 18 Challenge Level:

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

Age 14 to 16 Challenge Level:

A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base. Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate? Cosines Rule

Age 14 to 16 Challenge Level:

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement. Square Mean

Age 14 to 16 Challenge Level:

Is the mean of the squares of two numbers greater than, or less than, the square of their means? More Number Pyramids

Age 11 to 14 Challenge Level:

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

Age 14 to 16 Challenge Level:

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. . . . DOTS Division

Age 14 to 16 Challenge Level:

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}. Always Perfect

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . . Magic Squares II

Age 14 to 18

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

Age 14 to 16 Challenge Level:

I am exactly n times my daughter's age. In m years I shall be ... How old am I?