# Resources tagged with: Combinatorics

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### There are 41 results

Broad Topics > Decision Mathematics and Combinatorics > Combinatorics

### Semicircle

##### Age 16 to 18Challenge Level

Fourth challenge cipher

### A Fine Thing?

##### Age 16 to 18Challenge Level

Second challenge cipher

### Vital?

##### Age 16 to 18Challenge Level

Third challenge cipher

### Up a Semitone?

##### Age 16 to 18Challenge Level

Fifth challenge cipher

### Jluuis or Even Asutguus?

##### Age 16 to 18Challenge Level

Sixth challenge cipher

### Ip?

##### Age 16 to 18Challenge Level

Seventh challenge cipher

### An Introduction to Computer Programming and Mathematics

##### Age 16 to 18

This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

### The Eternity Puzzle

##### Age 16 to 18

A big prize was offered for solving The Eternity Puzzle, a jigsaw with no picture and every piece is the same on both sides. The finished result forms a regular dodecagon (12 sided polygon).

##### Age 14 to 18

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.

### Plum Tree

##### Age 14 to 18Challenge Level

Label this plum tree graph to make it totally magic!

### Magic Caterpillars

##### Age 14 to 18Challenge Level

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

### One Basket or Group Photo

##### Age 7 to 18Challenge Level

Libby Jared helped to set up NRICH and this is one of her favourite problems. It's a problem suitable for a wide age range and best tackled practically.

### Stage 5 Cipher Challenge

##### Age 16 to 18Challenge Level

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

### Factorial Fun

##### Age 16 to 18Challenge Level

How many divisors does factorial n (n!) have?

### W Mates

##### Age 16 to 18Challenge Level

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

### Magic W Wrap Up

##### Age 16 to 18Challenge 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.

### Transitivity

##### Age 16 to 18

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.

### Cube Net

##### Age 16 to 18Challenge Level

How many tours visit each vertex of a cube once and only once? How many return to the starting point?

### Russian Cubes

##### Age 14 to 16Challenge Level

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

### Snooker

##### Age 16 to 18Challenge Level

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

### Snooker Frames

##### Age 16 to 18Challenge Level

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

### Tangles

##### Age 11 to 16

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

### Lost in Space

##### Age 14 to 16Challenge Level

How many ways are there to count 1 - 2 - 3 in the array of triangular numbers? What happens with larger arrays? Can you predict for any size array?

##### Age 14 to 16Challenge Level

A walk is made up of diagonal steps from left to right, starting at the origin and ending on the x-axis. How many paths are there for 4 steps, for 6 steps, for 8 steps?

### Olympic Magic

##### Age 14 to 16Challenge Level

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

### Knight Defeated

##### Age 14 to 16Challenge 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. . . .

### Magic W

##### Age 14 to 16Challenge Level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### Penta Colour

##### Age 14 to 16Challenge Level

In how many different ways can I colour the five edges of a pentagon red, blue and green so that no two adjacent edges are the same colour?

### Doodles

##### Age 14 to 16Challenge Level

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

### Scratch Cards

##### Age 14 to 16Challenge Level

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

### Counting Binary Ops

##### Age 14 to 16Challenge Level

How many ways can the terms in an ordered list be combined by repeating a single binary operation. Show that for 4 terms there are 5 cases and find the number of cases for 5 terms and 6 terms.

### Postage

##### Age 14 to 16Challenge 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. . . .

### Symmetric Tangles

##### Age 14 to 16

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!

### Binomial Coefficients

##### Age 14 to 18

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

### Euler's Officers

##### Age 14 to 16Challenge Level

How many different ways can you arrange the officers in a square?

### N000ughty Thoughts

##### Age 14 to 16Challenge Level

How many noughts are at the end of these giant numbers?

### Ordered Sums

##### Age 14 to 16Challenge 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. . . .

### Snowman

##### Age 14 to 16Challenge Level

All the words in the Snowman language consist of exactly seven letters formed from the letters {s, no, wm, an). How many words are there in the Snowman language?

### In a Box

##### Age 14 to 16Challenge Level

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

### Deep Roots

##### Age 14 to 16Challenge Level

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$

### Molecular Sequencer

##### Age 14 to 18Challenge Level

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.