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Broad Topics > Decision Mathematics and Combinatorics > Algorithms

### Probably a Code?

##### Stage: 5 Challenge Level:

Is the regularity shown in this encoded message noise or structure?

### Odd One Out

##### Stage: 5 Short Challenge Level:

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

### Method in Multiplying Madness?

##### Stage: 3 Challenge Level:

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

### Funny Factorisation

##### Stage: 3 Challenge Level:

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

### Sorted

##### Stage: 5 Challenge Level:

How can you quickly sort a suit of cards in order from Ace to King?

### Ip?

##### Stage: 5 Challenge Level:

Seventh challenge cipher

### Jluuis or Even Asutguus?

##### Stage: 5 Challenge Level:

Sixth challenge cipher

### Up a Semitone?

##### Stage: 5 Challenge Level:

Fifth challenge cipher

### Semicircle

##### Stage: 5 Challenge Level:

Fourth challenge cipher

### Vital?

##### Stage: 5 Challenge Level:

Third challenge cipher

### A Fine Thing?

##### Stage: 5 Challenge Level:

Second challenge cipher

### Stage 5 Cipher Challenge

##### Stage: 5 Challenge Level:

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

### The Best Square

##### Stage: 4 and 5 Challenge Level:

How would you judge a competition to draw a freehand square?

### Weekly Challenge 41: Happy Birthday

##### Stage: 5 Challenge Level:

A weekly challenge concerning the interpretation of an algorithm to determine the day on which you were born.

### An Introduction to Computer Programming and Mathematics

##### Stage: 5

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.

### Peaches in General

##### Stage: 4 Challenge Level:

It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.

### Zeller's Birthday

##### Stage: 4 Challenge Level:

What day of the week were you born on? Do you know? Here's a way to find out.

### Unusual Long Division - Square Roots Before Calculators

##### Stage: 4 Challenge Level:

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

### Procedure Solver

##### Stage: 5 Challenge Level:

Can you think like a computer and work out what this flow diagram does?

### Geomlab

##### Stage: 3, 4 and 5 Challenge Level:

A geometry lab crafted in a functional programming language. Ported to Flash from the original java at web.comlab.ox.ac.uk/geomlab

### Stretching Fractions

##### Stage: 4 Challenge Level:

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

### On What Day Did it Happen?

##### Stage: 1, 2 and 3

Read this article to find out the mathematical method for working out what day of the week each particular date fell on back as far as 1700.

### Tournament Scheduling

##### Stage: 3, 4 and 5

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

### Divided Differences

##### Stage: 5

When in 1821 Charles Babbage invented the Difference Engine' it was intended to take over the work of making mathematical tables by the techniques described in this article.

### X Marks the Spot

##### Stage: 3 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

### Tis Unique

##### Stage: 3 Challenge Level:

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

### Kids

##### Stage: 3 Challenge Level:

Find the numbers in this sum

### Slippy Numbers

##### Stage: 3 Challenge Level:

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

### Vedic Sutra - All from 9 and Last from 10

##### Stage: 4 Challenge Level:

Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?

### Differs

##### Stage: 3 Challenge Level:

Choose any 4 whole numbers and take the difference between consecutive numbers, ending with the difference between the first and the last numbers. What happens when you repeat this process over and. . . .

### Medal Muddle

##### Stage: 3 Challenge Level:

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

### Alphabet Soup

##### Stage: 3 Challenge Level:

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

### Long Multiplication

##### Stage: 3 Challenge Level:

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

### Skeleton

##### Stage: 3 Challenge Level:

Amazing as it may seem the three fives remaining in the following skeleton' are sufficient to reconstruct the entire long division sum.

### Triangle Incircle Iteration

##### Stage: 4 Challenge Level:

Start with any triangle T1 and its inscribed circle. Draw the triangle T2 which has its vertices at the points of contact between the triangle T1 and its incircle. Now keep repeating this. . . .

### Route to Root

##### Stage: 5 Challenge Level:

A sequence of numbers x1, x2, x3, ... starts with x1 = 2, and, if you know any term xn, you can find the next term xn+1 using the formula: xn+1 = (xn + 3/xn)/2 . Calculate the first six terms of this. . . .