Other tags that relate to Nim
Generalising. Place value. Factors and multiples. Mathematical reasoning & proof. Working systematically. Creating and manipulating expressions and formulae. Number bases. Interactivities. Visualising. Games.There are 160 results
Broad Topics > Thinking Mathematically > Mathematical reasoning & proof
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?
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. . . .
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.
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?
Tower of Hanoi
Age 11 to 14
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.
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. . . .
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.
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?
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. . . .
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}.
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?
Is it Magic or Is it Maths?
Age 11 to 14
Challenge Level
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. . . .
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. . . .
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. . . .
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. . . .
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. . . .
Mindreader
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. . . .
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.
Gabriel's Problem
Age 11 to 14
Challenge Level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
What Numbers Can We Make Now?
Age 11 to 14
Challenge Level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
Seven Squares - Group-worthy Task
Age 11 to 14
Challenge Level
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?
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?
More Number Pyramids
Age 11 to 14
Challenge Level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
Cross-country Race
Age 14 to 16
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?
Adding All Nine
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. . . .
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.
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?
What Numbers Can We Make?
Age 11 to 14
Challenge Level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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. . . .
Geometric Parabola
Age 14 to 16
Challenge Level
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
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?
Concrete Wheel
Age 11 to 14
Challenge Level
A huge wheel is rolling past your window. What do you see?
Mediant Madness
Age 14 to 16
Challenge Level
Kyle and his teacher disagree about his test score - who is right?
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.
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. . . .
A Biggy
Age 14 to 16
Challenge Level
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
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?
Power Mad!
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.
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?
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?
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.
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. . . .
Common Divisor
Age 14 to 16
Challenge Level
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Perfectly Square
Age 14 to 16
Challenge Level
The sums of the squares of three related numbers is also a perfect square - can you explain why?
NRICH is part of the family of activities in the Millennium Mathematics Project.