I noticed that there are still a few followers of this prototype blog, so thought I'd post a message here.
Finally, I have launched GiftedMathematics.com as a website to help students learn the kind of mathematics found in mathematics competitions and challenges around the world.
There is a Prize Maths Question (PMQ) every Friday, so check the website for details.
There is also an Online Classroom. This is now under testing, so free places are available to the winners of the Friday PMQ!
Please spread the word to teachers and students. Please also note that this little blog will be closing down soon... too much information on here!!
There is also a Community on Google+ called Mathematics Competitions.
See you there!
Richard
Monday 7 January 2013
Friday 25 May 2012
Question 11: Everyone is Equal
In 2011, this M4 mathematics competition had only 10 competitors. The points awarded are the same as on the current Rules page. After 5 games everyone had the same number of points!
Is this possible? If so, provide one possible solution with the maximum possible total points. (Yes, everyone on zero points is a solution, but not maximal!)
The solution here must be in a grid showing the 10 competitiors and their point score for each of the 5 questions. There are many solutions, you need to find just one.
The easiest way is to use a spreadsheet so you can automatically calculate the totals.
Spreadsheets are really useful in questions such as this. If you don't know how to use one, and especially how to enter formulas into the cells, then come back in August when the full website will start. If you can't wait, then try here or here.
Good Luck!
SEND YOUR ANSWER TO q11pythagoras@giftedcentre.com [this email will be disabled in 7 days to avoid spam]
INCLUDE YOUR NAME AND SCHOOL IN YOUR ANSWER.
THE COMMENTS BOX BELOW IS LOCKED FOR 24 HOURS TO STOP STUDENTS POSTING THE ANSWERS!
ONCE THE COMMENTS ARE OPEN YOU ARE FREE TO DISCUSS THE QUESTION.
Is this possible? If so, provide one possible solution with the maximum possible total points. (Yes, everyone on zero points is a solution, but not maximal!)
The solution here must be in a grid showing the 10 competitiors and their point score for each of the 5 questions. There are many solutions, you need to find just one.
The easiest way is to use a spreadsheet so you can automatically calculate the totals.
Spreadsheets are really useful in questions such as this. If you don't know how to use one, and especially how to enter formulas into the cells, then come back in August when the full website will start. If you can't wait, then try here or here.
Good Luck!
SEND YOUR ANSWER TO q11pythagoras@giftedcentre.com [this email will be disabled in 7 days to avoid spam]
INCLUDE YOUR NAME AND SCHOOL IN YOUR ANSWER.
THE COMMENTS BOX BELOW IS LOCKED FOR 24 HOURS TO STOP STUDENTS POSTING THE ANSWERS!
ONCE THE COMMENTS ARE OPEN YOU ARE FREE TO DISCUSS THE QUESTION.
Question 12: The Crimson Room
To end our short journey through mathematical puzzles, here is a classic logic game: The Crimson Room.
The original can be found here:
http://crimson-room.net/
The website functions but the link to the actual online game does not seem to work as of writing. However, The Crimson Room is now available as a mobile app.
Enjoy!
... and remember, solving something yourself gives you a greater buzz than searching for someone else's answer!!
One day, you will need to solve something that nobody has solved.
The original can be found here:
http://crimson-room.net/
The website functions but the link to the actual online game does not seem to work as of writing. However, The Crimson Room is now available as a mobile app.
Enjoy!
... and remember, solving something yourself gives you a greater buzz than searching for someone else's answer!!
One day, you will need to solve something that nobody has solved.
Wednesday 16 May 2012
Question 5: A Dark Bridge
Here is another online puzzle. This time, unlike Question 4, we can write the solution in a symbolic form. The aim is to get all the people across the bridge before the lantern burns out. Instructions are on the first page.
Go to the bridge puzzle.
To write your answer, let's look at a nice and simple way to represent the people crossing the bridge. We shall represent each person by the number of minutes it takes them to cross the bridge.
If 3 and 8 cross together let's write this as (3,8).
If 6 crosses the bridge alone we can represent this with just one number (6).
So, for example, if 3 and 8 cross the bridge first, then 8 walks back alone, then 1 and 12 cross the bridge, then 3 walks back alone, we can show this simply as:
(3,8)(8)(1,12)(3)
This is obviously not a solution, and the puzzle has not been finished, it is just to show you a simple way for you to write the final solution.
A nice thing about this representation is that we can calculate the total minutes by adding the largest number in each bracket. In my example above, the total would be: 8 + 8 + 12 + 3 = 31. Way too high!
So, your final solution will be a string of brackets showing the sequence of your moves plus the toal number of minutes.
Good luck!
Go to the bridge puzzle.
To write your answer, let's look at a nice and simple way to represent the people crossing the bridge. We shall represent each person by the number of minutes it takes them to cross the bridge.
If 3 and 8 cross together let's write this as (3,8).
If 6 crosses the bridge alone we can represent this with just one number (6).
So, for example, if 3 and 8 cross the bridge first, then 8 walks back alone, then 1 and 12 cross the bridge, then 3 walks back alone, we can show this simply as:
(3,8)(8)(1,12)(3)
This is obviously not a solution, and the puzzle has not been finished, it is just to show you a simple way for you to write the final solution.
A nice thing about this representation is that we can calculate the total minutes by adding the largest number in each bracket. In my example above, the total would be: 8 + 8 + 12 + 3 = 31. Way too high!
So, your final solution will be a string of brackets showing the sequence of your moves plus the toal number of minutes.
Good luck!
Tuesday 15 May 2012
Question 4: Mouse Trap
Mathematics is about far more than numbers and shapes - it is fundamentally about patterns, and such patterns come in many forms. Imagine looking at a game of chess as it evolves from move to move. Every move changes the pattern on the chess board. At the end of the game the rules of chess determine whether the final pattern is a victory for white, for black or ends in a draw.
The mathematics of game theory aims to analyse games so as to find winning strategies. It has a wide range of applications in fields such as economics, biology and psychology. Now, chess is a game with simple rules yet complex strategies; far too hard for us to start with! So let's look at something simpler.
One of the favourite games at my after-school club is Mouse Trap. It is a simple game where a computer-operated mouse tries to escape from a hexagonal grid while you try to encircle it by blocking its path with bricks. You win if you manage to trap the mouse so it can no longer move; you lose if the mouse manages to reach the edge of the grid and thus escape.
Go to Mouse Trap now!
Play the game a few times and get a feel for how to trap the mouse.
This question is to write out a winning strategy. Be as precise as possible so that someone could write a computer program that takes your rules and applies them to every specific situation. This does not have to be a long essay! You should be able to describe your winning strategy in just four or five sentences.
One additional question: does your strategy win all the time?
Have fun!
The mathematics of game theory aims to analyse games so as to find winning strategies. It has a wide range of applications in fields such as economics, biology and psychology. Now, chess is a game with simple rules yet complex strategies; far too hard for us to start with! So let's look at something simpler.
One of the favourite games at my after-school club is Mouse Trap. It is a simple game where a computer-operated mouse tries to escape from a hexagonal grid while you try to encircle it by blocking its path with bricks. You win if you manage to trap the mouse so it can no longer move; you lose if the mouse manages to reach the edge of the grid and thus escape.
Go to Mouse Trap now!
Play the game a few times and get a feel for how to trap the mouse.
This question is to write out a winning strategy. Be as precise as possible so that someone could write a computer program that takes your rules and applies them to every specific situation. This does not have to be a long essay! You should be able to describe your winning strategy in just four or five sentences.
One additional question: does your strategy win all the time?
Have fun!
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