This is a neat game - it's called Icosien. If you know graph theory then essentially the goal of the game is to draw a Eulerian path (a path that visits each edge exactly once) in the given graph.
Icosien (game)
Aug 23, 2010
This is a neat game - it's called Icosien. If you know graph theory then essentially the goal of the game is to draw a Eulerian path (a path that visits each edge exactly once) in the given graph.
Self-Referential Aptitude Test
Aug 10, 2010
Jim Propp's self-referential aptitude test is quite interesting. It's a difficult puzzle but here are some hints/spoilers:
Click to read the comments on this entry...- Q1 states that Q1-5 must have at least one B.
- Q3 states that the number of Qs with answer E is 0-4.
- Q4 states that the number of Qs with answer A is 4-8.
- Q6 Answer to Q17 is C, D or E.
- Q8 states that the number of Qs with answer of A is 4-8.
- Q9 states that Q10 is A or Q11 is B or Q12 is C or Q13 is D or Q14 is E.
- Q11 states that there are 0-4 Qs before it with answer B.
- Q13 states that either 9,11,13,15,17 are A.
- Q14 states that the number of Qs with answer D are 6-10.
- Q17 states that the answer to Q6 is C, D, or E.
Conway's game of life (in html 5)
Jul 13, 2010
Check out the site sixfoottallrabbit.co.uk/gameoflife where you can play Conway's Game of Life (in html5). I was curious what the number 42 would produce, you know, since it's the answer to life and all.
This is my initial configuration above, the number 42.
After a while, it evolves into the configuration above.
Near the end, it produce 2 gliders (on the far right and far left) that travel on forever, along with a few blocks and behive.
I'm not sure what I was hoping for. I tried about 50 different configurations which all look like the number 42 to see if I could get a "gun" but so far all the ones I tried ended up with still lives, oscillators, and a few spaceships.
I think it'd be pretty cool if you could start with 42 and get a gun that continues to "create life"!
Click to read the comments on this entry...
This is my initial configuration above, the number 42.
After a while, it evolves into the configuration above.
Near the end, it produce 2 gliders (on the far right and far left) that travel on forever, along with a few blocks and behive.
I'm not sure what I was hoping for. I tried about 50 different configurations which all look like the number 42 to see if I could get a "gun" but so far all the ones I tried ended up with still lives, oscillators, and a few spaceships.
I think it'd be pretty cool if you could start with 42 and get a gun that continues to "create life"!
Math drinking games?
May 6, 2010
Saw this on Terry Tao's blog, it's a drinking game suggested by Mark Schnitzius that can promote mathematical thinking. Mark says:
Another silly drinking game is below:
Click to read the comments on this entry..."I was watching a travel show a while back -- they were in Korea, and a group of people were playing a drinking game. The way it worked was, one person was "it". This person says something like, "ready, set..." then points at one other player and calls out a number (call it x) between 2 and n (where n is the number of people playing). At the same time, everyone else also points at one other player. Then, for whatever number got call out, you jump that many steps from the "it" person, and that person has to drink. So if I call out "two" and point at Joe, and Joe points at Bob, then Bob has to drink.
I think the game is pretty interesting, mathematically, and could easily be adapted to be a game for kids. It's especially interesting when you relax the x<=n rule. One interesting thing I found: with n=3, if you call x=7, you are guaranteed to stick the player you initially point at, no matter who points to whom.
Some interesting questions to ponder about it:Hint for questions 1 and 2: prime numbers come in to play!"
- Without the x<=n rule, what is the smallest number the 'it' person can call that guarantees he will not stick himself?
- With the x<=n rule in place, what is the safest number to call for any given n, if the other players choose randomly?
- If you're TRYING to lose, what number should you call, both with and without the x<=n rule?
- What are the odds of winning or losing, for all the answers above?
Another silly drinking game is below:
Four color game
Apr 21, 2010
http://www.kongregate.com/games/Onefifth/flood-fill
In this game the goal is to fill in the pieces with at most 4 colors. Two pieces that touch can't share the same color. The game is mathematically interesting since the Four Color Theorem says that for any such 'map', four colors is enough.
Math games by an Oxford math prof
Dec 8, 2009
This Reuters article talks about Oxford professor Marcus du Sautoy and how he is an advisor for the mathy webgame website:
It's called Manga High and illustrated in the style of a Japanese comic.
Click to read the comments on this entry...It's called Manga High and illustrated in the style of a Japanese comic.
"He said the aim had been to make an integral part of the games "really challenging kinds of maths" and not just mental arithmetic.I went to the website and it's pretty damned cool!! Go have some fun!
A number of schools in London as well as Tennessee in the United States are trying out the website, which includes a game called "Save Our Dumb Planet," where children have to enter coordinates on a graph to aim a missile at an asteroid heading for the Earth.
"I think the teachers have been very impressed by the depth of the mathematics that we have managed to embed in these games. You can only get a high score if you do the maths," Du Sautoy said.
He said the game was a good example of the sort of maths that real scientists use, in this case to chart the course of a spaceship through the solar system."
Guess 2/3 of the average
Nov 11, 2009
The game is...
- you compete against some other people
- each of you guess one number from [0, 100]
- compute 2/3rd's of the average of the guessed numbers
- the winner is whoever is closest
(0.66666) x ([7 + 28 + 53 + 77] / 4) = 27.5
Therefore, whoever guessed 28 wins!!
So........... what number should you pick?
Of course the answer depends on your thought process. Let's take a look to see what numbers people picked:
So what number would you pick?
One should note that guessing any number that lies above 66.66 can NEVER be equal to 2/3rd's the average. Why is this true? Take the example that everyone picks 100. Then the average is 100. So 2/3rd's of this is 66.66. This is the highest that "2/3rd's the average" can be.
Thus, any rational player, would pick a number between [0, 66.67].
Now, any rational player would realize that everyone else is going to pick a number in [0, 66.67]. And thus the highest that 2/3rd's the average can be using numbers in [0, 66.67] is 44.444. So the rational person will not pick a number above 44.444, since there is no way it can be 2/3rd's the average.
Thus, any rational player, would pick a number between [0, 44.44].
Now you can see you can repeat this process and eventually get yourself down to [0, epsilon]. Thus, if everyone was rational, they would all pick the number 0, and hence, it would be a tie game.
However, strangely enough, not everyone can work the argument all the way down to 0. Hence, you have people picking 22 and 33 (see the spikes in the graph). The amazing thing is that people pick numbers like 100! There is no way 100 can win, so clearly these people don't understand the game at all, or never even thought about their answer. There is also a spike at 0, most likely by mathematicians and people from similar disciplines who are familiar with the problem. However, if they were really smart, they'd know that they can't win picking 0, since it's highly likely that not everyone will pick 0.
Click to read the comments on this entry...Of course the answer depends on your thought process. Let's take a look to see what numbers people picked:
So what number would you pick?
One should note that guessing any number that lies above 66.66 can NEVER be equal to 2/3rd's the average. Why is this true? Take the example that everyone picks 100. Then the average is 100. So 2/3rd's of this is 66.66. This is the highest that "2/3rd's the average" can be.
Thus, any rational player, would pick a number between [0, 66.67].
Now, any rational player would realize that everyone else is going to pick a number in [0, 66.67]. And thus the highest that 2/3rd's the average can be using numbers in [0, 66.67] is 44.444. So the rational person will not pick a number above 44.444, since there is no way it can be 2/3rd's the average.
Thus, any rational player, would pick a number between [0, 44.44].
Now you can see you can repeat this process and eventually get yourself down to [0, epsilon]. Thus, if everyone was rational, they would all pick the number 0, and hence, it would be a tie game.
However, strangely enough, not everyone can work the argument all the way down to 0. Hence, you have people picking 22 and 33 (see the spikes in the graph). The amazing thing is that people pick numbers like 100! There is no way 100 can win, so clearly these people don't understand the game at all, or never even thought about their answer. There is also a spike at 0, most likely by mathematicians and people from similar disciplines who are familiar with the problem. However, if they were really smart, they'd know that they can't win picking 0, since it's highly likely that not everyone will pick 0.
Physics Games
Nov 10, 2009
Need to waste some time?
This site www.physicsgames.net has a crapload of games that involve concepts like gravity, projectiles, constructions, "destructions", etc.
So far, I've played Splitter, Superstacker, MagicPen 1 & 2, Top Figures, Insurgo, Demolition City 1 & 2, and 99 Bricks, among others. Of course the site didn't make all these games, but the companies who do, let webmasters host them on their own site with certain restrictions.
My favorite is Cuber which is created by King.com :-D
Click to read the comments on this entry...So far, I've played Splitter, Superstacker, MagicPen 1 & 2, Top Figures, Insurgo, Demolition City 1 & 2, and 99 Bricks, among others. Of course the site didn't make all these games, but the companies who do, let webmasters host them on their own site with certain restrictions.
My favorite is Cuber which is created by King.com :-D
Eyeball math game
Oct 28, 2009
Apparently I'm pretty bad at using my eyes. You can try out this game at
Click to read the comments on this entry...
How to solve the sudokube
Oct 26, 2009
The Sudoku Cube is a ripoff of the Rubik's Cube, where each face has the numbers 1-9 instead of colours. The goal:
It was created in 2006 by some guy named Jay Horowitz in Ohio. You can buy it at Barnes and Noble and some other places. In what follows we briefly describe how to solve it...
put the numbers 1-9 on each side with no repetition
It was created in 2006 by some guy named Jay Horowitz in Ohio. You can buy it at Barnes and Noble and some other places. In what follows we briefly describe how to solve it...
Of course there are lots of variations, including cubes with 4x4x4, and naming variations are Sodokube, Roxdoku. If you want to solve it you need to realize there are a few different
variations on the cube, so depending which one you have, the solution
will be slightly different.
Step 1: Familiarize yourself with solving a Rubik's Cube. If you don't know how to solve the Rubik's cube, then you will have a LOT of trouble with the Sudokube (trust me!).
Step 2: Note the centres of each face of your cube. Some cubes have 5's in all the centres, others have varying numbers. As in the Rubik's cube, these centres will be fixed points and stay in place when you do the "moves".
Step 3: If you have the Rubik's cube algorithm memorized, you should now have no trouble at all solving the cube!!
The end!
Click to read the comments on this entry...Step 1: Familiarize yourself with solving a Rubik's Cube. If you don't know how to solve the Rubik's cube, then you will have a LOT of trouble with the Sudokube (trust me!).
Step 2: Note the centres of each face of your cube. Some cubes have 5's in all the centres, others have varying numbers. As in the Rubik's cube, these centres will be fixed points and stay in place when you do the "moves".
Step 3: If you have the Rubik's cube algorithm memorized, you should now have no trouble at all solving the cube!!
The end!
Hey guys, there is this game called "Tower Stack" or "Tower Bricks" or "Tower Blocks" (among other names) and you can play it on Facebook, or MindJolt Games, or Brothersoft Games (etc).
Here is a screenshot to show what I am talking about:
What you have to do is:
What you have to do is:
- - build tower as tall as possible
- - blocks swing at top and you click mouse to drop them
- - block will fall after you click and it MUST land on top of the block that you dropped previously (otherwise you lose a "life" - you have 3 "lives")
- - if you drop PERFECTLY on top, you get bonus points
- - as the tower gets bigger, it starts to shake back and forth making it harder to drop the blocks on top
Okay, let's do the first block. Just drop it anywhere on the platform as shown below.
Now drop the second block on top (see image below).
You now have 200 points, 100 from dropping the first block, and 100 from dropping the second block. Notice the 2 on the bottom left of the screen - that records the # of blocks dropped so far. Theoretically, you could go on forever dropping the blocks in this fashion scoring 100 points per drop. But as mentioned above you could get bonus points if you drop it perfectly on top as shown below:
Here we got 200 points instead of 100! Let's do another perfect drop:
Wowzers! 250 this time, instead 100 or 200! If we mess up it goes back to 100 as shown below:
Get 4 in a row and it's 300 points for that 4th block:
Get 6 in a row and it's 400 points for that 6th block:
So let's do some math! Basically the scoring works as follows:
What this means is that if you have n-1 perfect drops in a row, on the n'th perfect drop you will score an amazing 50n+100 points! (Note that for simplicity, we take the convention that the first drop was perfect).
Obviously one can figure out the optimal strategy now. If you keep getting imperfect drops, then you only get 100 points per drop:
But if you keep getting perfect drops you will score HUGE points on each drop. Below I had 19 perfect drops, so on that drop I got an outstanding 1050. If I get another perfect drop after that, the next one will be worth 1100.
It gets harder as you get lots of blocks. In the final image below I made it up to 132 blocks, but I didn't score that high because I just couldn't get in the rhythm of successive perfect drops.
So the question you should ask yourself is:
how high of a score can you get?
Well, let's assume you only have 100 blocks to drop until it becomes too hard and the game ends.
(i) If you do 100 imperfect drops, each drop will be worth 100 points. Thus, the score would amount to:
(ii) On the contrary, what if you have a perfect game so far. Then you would receive the following points:
If you said 5100 then you are right! This is the number of points you would get on the 100'th drop, and you can use the formula I presented to you above: 50n + 100.
Do you remember how to add up sums of numbers? Let's do it in general. Let's say you get n perfect drops in a row. How many total points would you get from those n drops? The total is:
This just follows from the sum formulas that you may have learned in either high school or university (note that the formula 50n+100 only works for n>=2, that's why we started the summation at 2). It's okay if you forgot the sum formulas or don't follow all the steps. The main point is that, if you get n PERFECT drops in a row the TOTAL number of points you will score is 25(n^2 + 5n - 2). Let's do an example. If n=5 then the total score you will have after 5 perfect drops is: 1200.
If you get 100 perfect drops in a row (which is possible!) then your total score will be:
That's an amazing score! I checked facebook and people have like 1,600,000, which seems totally impossible, but if you get 200 perfect drops in a row you're looking at a score of over 1,000,000. Now, mathematically it's possible, but come on!! Who is going to play a game for that long and be that dedicated to get so many perfect drops! I call cheats/hacks! (if it's a real score then I'm truly jealous)!
Click to read the comments on this entry...
Now drop the second block on top (see image below).
You now have 200 points, 100 from dropping the first block, and 100 from dropping the second block. Notice the 2 on the bottom left of the screen - that records the # of blocks dropped so far. Theoretically, you could go on forever dropping the blocks in this fashion scoring 100 points per drop. But as mentioned above you could get bonus points if you drop it perfectly on top as shown below:
Here we got 200 points instead of 100! Let's do another perfect drop:
Wowzers! 250 this time, instead 100 or 200! If we mess up it goes back to 100 as shown below:
Get 4 in a row and it's 300 points for that 4th block:
Get 6 in a row and it's 400 points for that 6th block:
So let's do some math! Basically the scoring works as follows:
Imperfect drops score:
100 points
Perfect drops score as follows:
(# perfect blocks in a row, score for that block)
(1, 100)
(2, 200)
(3, 250)
(4, 300)
(5, 350)
(6, 400)
(7, 450)
(8, 500)
...
(n, 50n + 100)
100 points
Perfect drops score as follows:
(# perfect blocks in a row, score for that block)
(1, 100)
(2, 200)
(3, 250)
(4, 300)
(5, 350)
(6, 400)
(7, 450)
(8, 500)
...
(n, 50n + 100)
What this means is that if you have n-1 perfect drops in a row, on the n'th perfect drop you will score an amazing 50n+100 points! (Note that for simplicity, we take the convention that the first drop was perfect).
Obviously one can figure out the optimal strategy now. If you keep getting imperfect drops, then you only get 100 points per drop:
But if you keep getting perfect drops you will score HUGE points on each drop. Below I had 19 perfect drops, so on that drop I got an outstanding 1050. If I get another perfect drop after that, the next one will be worth 1100.
It gets harder as you get lots of blocks. In the final image below I made it up to 132 blocks, but I didn't score that high because I just couldn't get in the rhythm of successive perfect drops.
So the question you should ask yourself is:
how high of a score can you get?
Well, let's assume you only have 100 blocks to drop until it becomes too hard and the game ends.
(i) If you do 100 imperfect drops, each drop will be worth 100 points. Thus, the score would amount to:
10,000 points.
(ii) On the contrary, what if you have a perfect game so far. Then you would receive the following points:
100 + 200 + 250 + 300 + 350 + 400 + 450 + ...
Can you see what the last number will be in this sum?If you said 5100 then you are right! This is the number of points you would get on the 100'th drop, and you can use the formula I presented to you above: 50n + 100.
Do you remember how to add up sums of numbers? Let's do it in general. Let's say you get n perfect drops in a row. How many total points would you get from those n drops? The total is:
This just follows from the sum formulas that you may have learned in either high school or university (note that the formula 50n+100 only works for n>=2, that's why we started the summation at 2). It's okay if you forgot the sum formulas or don't follow all the steps. The main point is that, if you get n PERFECT drops in a row the TOTAL number of points you will score is 25(n^2 + 5n - 2). Let's do an example. If n=5 then the total score you will have after 5 perfect drops is: 1200.
If you get 100 perfect drops in a row (which is possible!) then your total score will be:
262,450
World of Warcraft - Negative gold problem
Sep 12, 2009
There is a flaw in World of Warcrafts statistics for "Total gold acquired". A couple years ago, players discovered that the most a character can hold is 2^31 (or 2147483648) copper pieces of currency. This is what is known as the "gold cap" in World of Warcraft. A single character cannot hold more gold than this in his backpack, otherwise an error is reported.
Unfortunately, the statistics Blizzard keeps works differently. If you
were to acquire more than 2^31 copper pieces, it basically goes into
the negatives. That is, it will go as:
..., 2147483646, 2147483647, 2147483648, -2147483648, -2147483647, ....
and back to 0.
I tried this and managed to get into the negatives, and eventually get it back to 0... and then up to 2147483648 again lol. I wonder if blizzard has a counter to see how many times you went into the negatives and got back up to 0.
Click to read the comments on this entry......, 2147483646, 2147483647, 2147483648, -2147483648, -2147483647, ....
and back to 0.
I tried this and managed to get into the negatives, and eventually get it back to 0... and then up to 2147483648 again lol. I wonder if blizzard has a counter to see how many times you went into the negatives and got back up to 0.
How to play STRIMKO
Sep 4, 2009
I thought it would be fun to create a video on "How to play strimko." It's just like Sudoku but more fun!! Hopefully the creators over at strimko.com don't mind me posting it on Youtube ^_^
You can view the video here (and you can play the fun game at strimko.com).
Click to read the comments on this entry...You can view the video here (and you can play the fun game at strimko.com).
Cool game - 20 questions - and how it works
Sep 2, 2009
Twenty Questions is a popular game which encourages deductive reasoning. Usually, one person is chosen to be the answerer. That person chooses a subject but does not reveal this to the others. All other players are questioners. They each take turns asking a question which can be answered with a simple "Yes" or "No". Lying is not allowed, as it would ruin the game. If a questioner guesses the correct answer, that questioner wins and becomes the answerer for the next round. If 20 questions are asked without a correct guess, then the answerer has stumped the questioners and gets to be the answerer for another round.
The above game is called 20Q and you can play it online at 20Q.net.
Now for some math:
The game is often used as an example when teaching students about information theory. Mathematically, if each question is structured to eliminate half the objects, 20 questions will allow the questioner to distinguish between 2^20 or 1,048,576 objects. Thus, the best strategy for 20 Questions is to ask questions that will split the field of remaining possibilities roughly in half each time. This process is analogous to a binary search algorithm in computer science.
Click to read the comments on this entry...Now for some math:
The game is often used as an example when teaching students about information theory. Mathematically, if each question is structured to eliminate half the objects, 20 questions will allow the questioner to distinguish between 2^20 or 1,048,576 objects. Thus, the best strategy for 20 Questions is to ask questions that will split the field of remaining possibilities roughly in half each time. This process is analogous to a binary search algorithm in computer science.
Cool Math Games
Aug 28, 2009
The net has a great amount of interactive cool maths games. Below are a few sites worth taking a look at. Most of the math games are fun for all ages and they are all absolutely free.
1. http://www.mathplayground.com/games.html
2. http://www.coolmath-games.com/
3. http://resources.kaboose.com/games/math2.html
4. http://www.primarygames.com/math.htm
5. http://cemc2.math.uwaterloo.ca/mathfrog/
Click to read the comments on this entry...1. http://www.mathplayground.com/games.html
2. http://www.coolmath-games.com/
3. http://resources.kaboose.com/games/math2.html
4. http://www.primarygames.com/math.htm
5. http://cemc2.math.uwaterloo.ca/mathfrog/
Checkmate! Tough Dice Game
Aug 25, 2009The impossible (yet so simple) dice game.
Play the game:
Instructions:
- Press the "Roll dice!" button to start.
- Try and determine how many moves there are until checkmate.
- Press the "Display Answer!" button to see if you are right.
- Once you have figured it out, don't spoil the fun for others!
Background:
This game is based on the "Petals Around the Rose" dice game. Both games are easy in the sense that once you know the "secret", you can easily determine the answer in seconds. After hearing of this game, I was able to figure out the secret immediately. Just remember, as in "Petals Around the Rose", the name of the game is important. Note however, you do not actually need to know anything about chess to figure out the secret.Petals Around the Rose - Dice Game
Aug 24, 2009Play the game here:
Instructions:
- Press the "Roll dice!" button to start.
- Try and determine how many petals are around the rose.
- Press the "Display Answer!" button to see if you are right.
- Once you have figured it out, don't spoil the fun for others!
Strimko is a brand new logic puzzle with numbers, just like Suduko. It is based on Latin squares described by Leonhard Euler in the 18th century.
The rules are simple: each row and column of an n x n grid must contain the numbers 1, 2, ..., n exactly once (just like in Sudoku ), and each "stream" (connected path in the grid) must also contain the numbers 1, 2, ..., n exactly once.
Strimko is created and developed by The Grabarchuk Family. It's basically a generalization of Sudoku as Sudoku can be thought of as having 9 streams.
You can play the addicting game at their website: strimko.com
Educational games - Planarity.net
Aug 12, 2009
We had a math camp at University and needed something educational for the elementary school kids. We chose the topic graph theory and decided to teach them about planar graphs. It turns out thathttp://www.planarity.net has this great flash game that you can play where you have to arrange the vertices such that no edges overlap. The kids sure had fun with it. It was created by John Tantalo, a CS undergrad at Case Western Reserve University.
Another task we had on paper was for the kids to design an air flight pathway between airports, where the airports are fixed 'vertices', and the flight paths ('edges') can't overlap to avoid crashes.
Click to read the comments on this entry...Another task we had on paper was for the kids to design an air flight pathway between airports, where the airports are fixed 'vertices', and the flight paths ('edges') can't overlap to avoid crashes.How to Solve a Rubik's Cube Videos
Aug 3, 2009
Dan Brown takes us inside on how to solve the Rubik's Cube:
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