Today we are visiting a specific instance of a well-known basic mathematics game, the 24 Game. The "24 Game" is usually played with younger students because it helps them develop skills related to the basic arithmetic operations.
Today is the day! Today is the day we take our APL programs and interpret them, so that something like ÷ 1 2 3 -⍨ 1.1 2.2 3.3 can output 10 5 3.33333333.
Take out a piece of paper and a pencil, I am going to ask you to write some letters in your sheet of paper and then I am going to challenge you to fold the sheet of paper... with a twist!
\(n\) mathematicians with numbered party hats gather around in a circle... It is a matter of life or death!
Let's build a simple APL interpreter! APL is an array-oriented programming language I picked up recently. The ease with which I can write code related to mathematics, its strange built-ins (which look like ⍴, ⍨, ⍒ or ⍣) and the fact that it is executed from right to left make it a fresh learning experience!
There's 100 drawers and 100 shuffled balls. Can you find the one I choose?
Can you cover all of the rational numbers in [0, 1] with tiny intervals?
Split the numbers 0, 1, ..., 15 into two sets with sum interesting properties!
In high school I had a colleague that had his birthday on the same day as I did. What a coincidence, right? Right..?
Given some paper squares, can you slice them and then glue them back together to form a single square?
Is it true that every integer you can think of has a multiple written out only with \(0\)s and \(1\)s?
I find the problem in this post rather fun to think about because it is a problem about a game that can actually be played between two players.
In this post we will talk about three different, all very common, ways of writing proofs: proofs by construction, by contrapositive and by contradiction.
This problem is a really interesting problem I solved two times. The first time I solved it I failed to prove exactly how it works... then some years later I remembered the problem statement and was able to solve it properly. Let's see how you do!
