Resources tagged with: Combinatorics

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There are 41 results

Broad Topics > Decision Mathematics and Combinatorics > Combinatorics

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?

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?

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?

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?

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).

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.

Semicircle

Age 16 to 18Challenge Level

Fourth 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.

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?

Jluuis or Even Asutguus?

Age 16 to 18Challenge Level

Sixth challenge cipher

Ip?

Age 16 to 18Challenge Level

Seventh challenge cipher

Up a Semitone?

Age 16 to 18Challenge Level

Fifth challenge cipher

Vital?

Age 16 to 18Challenge Level

Third challenge cipher

A Fine Thing?

Age 16 to 18Challenge Level

Second challenge cipher

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?

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.

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.

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.

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.

N000ughty Thoughts

Age 14 to 16Challenge Level

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

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?

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?

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?

Euler's Officers

Age 14 to 16Challenge Level

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

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?

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?

Binomial Coefficients

Age 14 to 18

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

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.

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!

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?

Factorial Fun

Age 16 to 18Challenge Level

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

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?

Deep Roots

Age 14 to 16Challenge Level

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

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. . . .

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.

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.

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. . . .

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.