Other tags that relate to Tree Graphs
Mathematical reasoning & proof. Visualising. Working systematically. Number theory. Networks/Graph Theory. Generalising. Combinatorics. Topology. Inequalities. Creating and manipulating expressions and formulae.There are 77 results
Broad Topics > Thinking Mathematically > Generalising
Interpolating Polynomials
Age 16 to 18
Challenge Level
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
Steel Cables
Age 14 to 16
Challenge Level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Rational Roots
Age 16 to 18
Challenge Level
Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
Take Three from Five
Age 11 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?
Sums of Pairs
Age 11 to 16
Challenge Level
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Loopy
Age 14 to 16
Challenge Level
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
Nim
Age 14 to 16
Challenge Level
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Can it Be?
Age 16 to 18
Challenge Level
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
Shape and Territory
Age 16 to 18
Challenge Level
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
Winning Lines
Age 7 to 16
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Hypotenuse Lattice Points
Age 14 to 16
Challenge Level
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
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.
One, Three, Five, Seven
Age 11 to 16
Challenge Level
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
Generally Geometric
Age 16 to 18
Challenge Level
Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.
Games Related to Nim
Age 5 to 16
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Pentanim
Age 7 to 16
Challenge Level
A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
More Twisting and Turning
Age 11 to 16
Challenge Level
It would be nice to have a strategy for disentangling any tangled ropes...
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
Jam
Age 14 to 16
Challenge Level
To avoid losing think of another very well known game where the patterns of play are similar.
Multiplication Arithmagons
Age 14 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Partly Painted Cube
Age 14 to 16
Challenge Level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Building Gnomons
Age 14 to 16
Challenge Level
Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
Mystic Rose
Age 14 to 16
Challenge Level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Sliding Puzzle
Age 11 to 16
Challenge Level
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Maximum Scattering
Age 16 to 18
Challenge Level
Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
A Tilted Square
Age 14 to 16
Challenge Level
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
Harmonic Triangle
Age 14 to 16
Challenge Level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Absurdity Again
Age 16 to 18
Challenge Level
What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?
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?
Searching for Mean(ing)
Age 11 to 16
Challenge Level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Pareq Calc
Age 14 to 16
Challenge Level
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
Cyclic Triangles
Age 16 to 18
Challenge Level
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
Plus Minus
Age 14 to 16
Challenge Level
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
For Richer for Poorer
Age 14 to 16
Challenge Level
Charlie has moved between countries and the average income of both has increased. How can this be so?
Pair Products
Age 14 to 16
Challenge Level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Generating Triples
Age 14 to 16
Challenge Level
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Lower Bound
Age 14 to 16
Challenge Level
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Semi-square
Age 14 to 16
Challenge Level
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
Converging Means
Age 14 to 16
Challenge Level
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
Chocolate 2010
Age 14 to 16
Challenge Level
First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
Square Pizza
Age 14 to 16
Challenge Level
Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
Pinned Squares
Age 14 to 16
Challenge Level
What is the total number of squares that can be made on a 5 by 5 geoboard?
NRICH is part of the family of activities in the Millennium Mathematics Project.