Resources tagged with Mathematical reasoning & proof similar to Behind the Rules of Go:
Other tags that relate to Behind the Rules of Go
Games. Mathematical reasoning & proof. Networks/Graph Theory. Trial and improvement. Working systematically. Visualising. Combinatorics. Euler's formula. Interactivities. Creating expressions/formulae.There are 164 results
Knight Defeated
Stage: 4 Challenge Level: 
The knight's move on a chess board is 2 steps in one direction and one step in the other direction. Prove that a knight cannot visit every square on the board once and only (a tour) on a 2 by n board. . . .
Sprouts
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. . . .
Cube Net
Stage: 5 Challenge Level:
How many tours visit each vertex of a cube once and only once? How many return to the starting point?
Euler's Formula and Topology
Stage: 4 and 5
Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the. . . .
Yih or Luk Tsut K'i or Three Men's Morris
Stage: 3, 4 and 5 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. . . .
Transitivity
Stage: 5
Suppose A always beats B and B always beats C, then would you expect A to beat C? Not always! What seems obvious is not always true. Results always need to be proved in mathematics.
Whole Number Dynamics II
Stage: 3, 4 and 5
This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.
Magic W Wrap Up
Stage: 5 Challenge Level:
Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.
Quadratic Harmony
Stage: 5 Challenge Level:
Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
Postage
Stage: 4 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. . . .
Geometry and Gravity 2
Stage: 3, 4 and 5
This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.
Pair Squares
Stage: 5 Challenge Level:
The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.
AMGM
Stage: 4 Challenge Level:
Choose any two numbers. Call them a and b. Work out the arithmetic mean and the geometric mean. Which is bigger? Repeat for other pairs of numbers. What do you notice?
Mediant
Stage: 4 Challenge Level:
If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.
A Computer Program to Find Magic Squares
Stage: 5
This follows up the 'magic Squares for Special Occasions' article which tells you you to create a 4by4 magicsquare with a special date on the top line using no negative numbers and no repeats.
Whole Number Dynamics I
Stage: 3, 4 and 5
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
Proof Sorter - Quadratic Equation
Stage: 4 and 5 Challenge Level:
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
Exhaustion
Stage: 4 Challenge Level:
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
Magic Squares II
Stage: 4 and 5
An article which gives an account of some properties of magic squares.
Where Do We Get Our Feet Wet?
Stage: 5
Jenny Piggott chose this article. Professor Körner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
Whole Number Dynamics IV
Stage: 4 and 5
Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?
Picture Story
Stage: 4 Challenge Level:
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Unit Interval
Stage: 4 and 5 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?
Whole Number Dynamics III
Stage: 5
In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.
Impossible Sandwiches
Stage: 3, 4 and 5
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.
Leonardo's Problem
Stage: 4 and 5 Challenge Level:
A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
Proof Sorter - Geometric Series
Stage: 5 Challenge Level:
This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.
Sperner's Lemma
Stage: 5
An article about the strategy for playing The Triangle Game which appears on the NRICH site. It contains a simple lemma about labelling a grid of equilateral triangles within a triangular frame.
The Great Weights Puzzle
Stage: 4 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?
Iffy Logic
Stage: 4 Short Challenge Level:
Can you rearrange the cards to make a series of correct mathematical statements?
Diverging
Stage: 5 Challenge Level:
Show that for natural numbers x and y if x/y > 1 then x/y>(x+1)/(y+1}>1. Hence prove that the product for i=1 to n of [(2i)/(2i-1)] tends to infinity as n tends to infinity.
Some Circuits in Graph or Network Theory
Stage: 4 and 5
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
Tree Graphs
Stage: 4 Challenge Level:
A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree. . . .
Direct Logic
Stage: 5 Challenge Level:
Can you work through these direct proofs, using our interactive proof sorters?
Problem Solving, Using and Applying and Functional Mathematics
Stage: 1, 2, 3, 4 and 5 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.
Doodles
Stage: 4 Challenge Level:
A 'doodle' is a closed intersecting curve drawn without taking pencil from paper. Only two lines cross at each intersection or vertex (never 3), that is the vertex points must be 'double points' not. . . .
Russian Cubes
Stage: 4 Challenge Level:
How many different cubes can be painted with three blue faces and three red faces? A boy (using blue) and a girl (using red) paint the faces of a cube in turn so that the six faces are painted. . . .
Notty Logic
Stage: 5 Challenge Level:
Have a go at being mathematically negative, by negating these statements.
Proof Sorter - Sum of an AP
Stage: 5 Challenge Level:
Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing
Symmetric Tangles
Stage: 4
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
Perfectly Square
Stage: 4 Challenge Level:
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Can it Be
Stage: 5 Challenge Level:
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
Pythagorean Triples II
Stage: 4 and 5
This is the second article on right-angled triangles whose edge lengths are whole numbers.
Pythagoras Proofs
Stage: 4 Challenge Level:
Can you make sense of these three proofs of Pythagoras' Theorem?
Take a Square II
Stage: 4 Challenge Level:
What fractions can you divide the diagonal of a square into by simple folding?
Mouhefanggai
Stage: 4
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
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