Constructions which are independent of your unit (In Progress)
A few weeks ago I remembered a puzzle I once saw known as the crossed ladders theorem. The way I remembered was:I have two poles sticking out of the ground. One is 4m tall and the other is 6m tall. I...
View ArticleArithmetic progressions of polygonal numbers
Recently I have thought a lot about the square numbers and in particular arithmetic progressions of squares. Today I wondered what properties of squares followed over to triangle numbers. Fermat proved...
View ArticleA conjecture and a prize
Today I would like to discuss a conjecture I recently made in additive combinatorics. I will award £5 for a solution to this conjecture. First, we need some notation.Let $A$ be a subset of the natrual...
View ArticleMore ABC thoughts
Last time I talked about the abc conjecture. I would like to mention it a little more today. Just to recap here is the conjecture again,let $\epsilon>0.$ The abc conjecture states that there are...
View ArticleAs easy as ABC
I haven't done a blog post for a very longtime so I think I should return with something I think is special. I.e. THE ABC CONJECTURE!The abc conjecture is a quite famous (and possibly solved but im not...
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Primes which are the sum of two cubes
I was recently reminded of Fermats result on when a prime number can be expressed as the sum of two squares. This then got me thinking on when a prime can be wrote as the sum of two cubes. I start by...
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An interestingish Diophantine equation
It is someone in my offices 26th birthday today. Last year he was a square age and next year he will be a cube age. I wondered whether this would ever happen again for him and this led me to solve the...
View ArticlePrincess on a train
Suppose the princess has escaped the confines of a graph (See here and here). She is now on a train and prince must once again come up with a strategy to capture her.I was first told about this puzzle...
View ArticlePrisoners in hats
Situations about people wearing hats is a common occurence in puzzles. One of my favourite puzzles is one of these.A prison has just recieved $n$ new prisoners, $n\geq 2$. Unfortunately the prison is...
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Tic-Tac-Othello
Today I would like to talk about a game myself and a friend invented. This is our second greatest collabaration after wispa bets. Its a version of tic-tac-toe incorporating the game othello(also known...
View ArticlePrincess on a graph and the Cyclic Knight part 1
This is going to be a very short blog post about a problem I have been working on. When a solution is found I will do an update.This is a generalisation of the princess on a graph puzzle. For those of...
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Equi Shape things
I saw a square today whose sides were labeled 4cm. I thought "Thats nice. Its perimeter and area are the same!" That then got me thinking into what the side lentgh of other polygons must be in order...
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Edgey graphs: Some unsolved problems from a 6 year old version of myself
Below I have a collection of graph like objects:You have probably noticed that these are not actual graphs since some edges connect vertices into other edges. I am terming these objects as edgey...
View ArticleAn interesting limit
Today me and Keith made an interesting discovery \[\lim_{\lambda\rightarrow\infty}\left(\frac{\lambda}{1+\lambda}\right)^{\lambda}=\frac{1}{e}\] and yet...
View ArticlePlaying cards
I bought a pack of cards yesterday. They faro shuffled face up and not face down :(
View Article![Mac Miller – The Divine Feminine (10th Anniversary) [iTunes Plus M4A]](http://is1-ssl.mzstatic.com/image/thumb/Music211/v4/a5/f7/d9/a5f7d909-56a4-813b-15ce-fc50e32afb7d/093624817154.jpg/296x296bb.webp)
