Digital Wipeout can be played by up to 6 players.

Visit our download page Apple Mac Applications

and also our download page Apple Mac Games

Read a Summary of the BBC's Horizon programme on Fermat's Last Theorem. The complete Transcript is also available. For CSYS students doing Paper 2 visit these excellent Graph Theory Tutorials. This is Web-based interactive instruction at its best! Visit the extraordinary The Science & Mathematics of Lighthouses A comprehensive list of links to Mathematical Societies world wide

All our weekly links are added to our Links for Teachers or Links for Students Pages.

Prime numbers are notorious for producing apparent patterns that eventually fail...

3, 31, 331, 3331, 33331, 333331, 3333331 and 33333331 are all Prime numbers... now do the following calculation: 17 x 19607843 and be amazed.

In mathematics the symbol ! is called the factorial sign. An example of its use is: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 Check the following calculations: 3! - 2! + 1! = 5 4! - 3! + 2! - 1! = 19 5! - 4! + 3! - 2! + 1! = 101 6! - 5! + 4! - 3! + 2! - 1! = 619 7! - 6! + 5! - 4! + 3! - 2! + 1! = 4421 9! - 8! + 6! - 5! + 4! - 3! + 2! - 1! = 35899 All these answers are Prime numbers. Now calculate the next value and compare it with 79 x 4139 and be amazed.

If you discover a prime number pattern that doesn't continue (or does it?) then we want to know. E-mail us at madrascollege.maths@fife.gov.uk and we will publish them here. You will find the List of Primes useful when you search for patterns.

In the Game of Wyt Queens some chess queens have become sociable at the expense of their movement on the board. They are gathering in the top left square and you are hoping that you are the one to show the last queen into the meeting!

 

Visit our mathematical games section which contains another 17 games.

Last week's Amazing Number Fact No 46 on Bulgarian Patience raised a lot of interest. If you wish to incorporate the idea into a lesson then you will get plenty advice on this Web Page.

Ontimers can turn your Mac into talking timer.

Think Ahead. A strategic board game invoving integers.

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and also our download page Apple Mac Games

Take a number of counters (or coins or matches etc) and arrange them into heaps. You are allowed one large heap or lots of heaps of just one counter or any arrangement inbetween these two extremes. You now proceed by carrying out the following procedure:

Take one counter from each existing heap and create a new heap

Repeat this procedure again and again observing the pattern of heaps that is produced. For example here is the procedure carried out with 6 counters initially arranged into two heaps of three:

Notice that the pattern of heaps is now the same. Repeating the procedure does not change the number or sizes of the heaps. Was this peculiar to starting with 6 counters? What other numbers of starting counters produce this constant pattern? Does changing the initial number of heaps affect the final outcome? Explore Bulgarian Patience and be amazed!!

 

If you have answers, discoveries, new questions etc to do with this Number Fact then...

E-mail us at madrascollege.maths@fife.gov.uk

...and we will publish them here.

Read our previous Amazing Number Facts

 

This week's game is White Knight. You may recall the White Knight that Alice met in 'Through the looking glass' who was always falling off his horse and losing his boxes and bags. In this game you must try to get the White Knight home with no luggage!

 

Visit our mathematical games section which contains another 16 games.

New challenges for S1-S3 and S4-S6 with a deadline of 22nd January.

The unsolved problems become Tough Nuts and may be tackled at any time.

Some excellent attempts at solutions by our students led to some published work in the current The Interact Magazine. Contributions were as follows:

Jonathan Hyne, Elizabeth Whitmore and James Wylde	S6	As Easy as 1,2,3
Tom Davie, Ella Ryan and James Wylde	S6	Wrapping Gifts

Congratulations to these students for their efforts.

 

Chac and links to the Mayan Calendar

This software allows you to explore the complexities and delights of the Mayan Calendar. The Mayan Glyphs are quite stunning ... it is a true work of art. Necessary background information concerning how the Maya constructed their calendar can be found by exploring the links that we have provided. Enjoy your exploration!

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and also our download page Apple Mac Games

What is special about the set of numbers 1, 3 and 8 ? Let's take all the possible products of pairs of these numbers:

1 x 3 = 3 = 42 - 1

1 x 8 = 8 = 32 - 1

3 x 8 = 24 = 52 - 1

They are all one less than a square. Can you find any other triples of whole numbers that have this property? Is it possible to find a set of four numbers with this property? Yes it is. We need only add the number 120 to 1, 3 and 8 :

1 x 3 = 3 = 42 - 1	1 x 120 = 120 = 112-1
1 x 8 = 8 = 32 - 1	3 x 120 = 360 = 192-1
3 x 8 = 24 = 52 - 1	8 x 120 = 960 = 312-1

Can you discover other sets of 4 whole numbers that have this property? Is it possible to find a set of five whole numbers with this property? Amazingly the answer is NO!! This was only proved in the year 1969.

 

If you have answers, discoveries, new questions etc to do with this Number Fact then...

E-mail us at madrascollege.maths@fife.gov.uk

...and we will publish them here.

Read our previous Amazing Number Facts

 

Mathematical Games

The Game of Sprouts was invented in 1967 by Princeton mathematician John H. Conway and by Michael S. Paterson, when both were at the University of Cambridge in England. Here is a quote from Conway:

"The day after sprouts sprouted, it seemed that everyone was playing it, at coffee or tea times, there were little groups of people peering over ridiculous to fantastic sprout positions."

We have a Sprouts Page with some new links concerning the game.

 

Visit our mathematical games section which contains another 12 games.

Download Site for Big Friendly Calculator

A basic calculator for the Mac with BIG buttons and a BIG display. The novelty feature is that it talks describing your calculation as you perform it. It also has two windows, a normal display and a window that shows you the calculation. This would be good for the less able student. It's good fun!

Visit our download page Apple Mac Applications

and also our download page Apple Mac Games

Links of the Week

This week we give two links concerning the wonderful SOMA CUBE puzzle:

Thorleif's SOMA PAGE contains a wealth of information

The Soma Figure Gallery contains plenty of constructions to challenge your puzzling skills

The Ultimate Palindrome

What is a Palindromic Number? Examples are 11, 123321 and 2002. They read the same backwards as forwards. This is the number equivalent of a Palindrome which is a word which reads the same forwards and backwards. Hannah is an example.

Pick a number, reverse its digits and add the resulting number to the original number. If the answer is not palindromic then repeat the process. For example let's start with 87:

Step 1:	87 + 78 = 165	not palindromic so...
Step 2:	165 + 561 = 726	not palindromic so...
Step 3:	726 + 627 = 1353	not palindromic so...
Step 4:	1353 + 3531 = 4884	palindromic!

You might like to explore the result of doing this process to several other small numbers. Do all the numbers that you try end up with a palindromic number?

196 is a particularly stubborn number. Nobody knows whether eventually doing this reversal and adding process with 196 yields a palindromic number. Here is a quote from an account written by John Walker on May 25th 1990. He had written a computer program in an attempt to determine the outcome for the number 196:

"For almost three years the process of reversal and addition continued. Last night, at five minutes before midnight, the program printed the message: 'Stop point reached on pass 2415836. Number contains 1000000 digits.' and exited. The built-in endpoint had been reached; after 2,415,836 reversals and additions, 196 had grown to a number of 1,000,000 digits without ever yielding a palindrome. Does it ever produce one? Still, nobody knows."

Recently computer tests have continued up to nearly 9.5 million steps yielding a 4.9 million digit number which is not yet palindromic! The search no doubt continues!!

 

If you have answers, discoveries, new questions etc to do with this Number Fact then...

E-mail us at madrascollege.maths@fife.gov.uk

...and we will publish them here.

Read our previous Amazing Number Facts

 

Mathematical Games

We present another four new games this week. All these games make an excellent resource for discussing strategy especially if you consider simple games... eg small boards, few counters etc

Col A map colouring game

Nim A game where you help yourself from several heaps of counters

Northcott's Game Attempt to trap all your opponent's pieces

Seating Couples Watch who sits beside who as you host a dinner party!

Our mathematical games section contains another 12 games.

Download Snakey Math

This demo version allows two players to race snakes towards the correct answer to an integer product. A great idea ... highly motivational.

Try RummyTile.

RummyTile is a game for 2 to 4 players in which the object is to eliminate all your tiles by forming them into sets of runs and groups. There is room for strategic thinking in the creative way that runs and sets may be broken up and reassembled on the board. There is a separate file that accompanies the game which explains the detailed rules and some hints about strategy.

Visit our download page Apple Mac Applications

and also our download page Apple Mac Games

Interested in The period length of the decimal expansion of a fraction ?

Interested in Pascal's Triangle? Then visit Arithmetic properties of Binomial Coefficients

Interested in proving Pythagoras' Theorem? Pythagorean Theorem has 29 different proofs!

More Mathematics than Science has some useful interactive demonstrations (your machine will need to be able to run Java Applets for these to be functional)

Ordered Digital Equations

Using two digits:81 = 8 + 1

Using three digits:

33 + 3 = 33 - 3

2(3+2) = 2 x 32

2(5 + 5) = 25 - 5

6 + 5x4 = 6x5 -4

361 = 3x6 + 1

(6 + 2)2 = 62 + 2

1 + 2 + 3 = 1 x 2 x 3

4 x 4 x 4 = 44 / 4

Using four digits..... ?? Can you discover other examples?

 

If you have answers, discoveries, new questions etc to do with this Number Fact then...

E-mail us at madrascollege.maths@fife.gov.uk

...and we will publish them here.

Read our previous Amazing Number Facts

 

We present three new games this week:

Ski-jumps Keep your skiers on the slope as long as you can

Toads & Frogs Make your creatures jump along the lanes to stop your opponent

Cutcake Don't be left with just crumbs!

Our mathematical games section contains another 9 games.