Dork Scratchings

P(l)ayoff table What's the best strategy for taking or defending penalty kicks?  Essentially there are three options for each player: go left, right or centre.  But what proportion of the time should each player take each of these options? We can try to answer this with a toy model and see what happens.  In this model the goal is always saved if the choices match and is always conceded if they don't.  What makes this model interesting is the "utility" of each outcome to each player. We could choose 1:0 to the striker for a goal and 1:0 to the goalie for a save, but we can make things more realistic by applying a bit of psychology.  Let's face it: if the goalie doesn't move and the ball goes left or right s/he will look pretty stupid.  For that reason I have given the goalie a minus one in this case.  Likewise if the striker shoots towards the middle and the goal is saved then the striker will look silly, so in that case he or she gets a minus one inste

Can you cover the 34 squares with 17 2x1 dominoes? Here's a puzzle I was shown by my lecturer Professor Schofield back in Bristol, last century: Make a 6x6 grid and remove two diagonally opposite squares so that you're left with 34 squares.  Given 17 two by one dominoes, can you cover the remaining area?  The illustration above shows one failed attempt. S C R O L L D O W N F O R T H E S O L U T I O N Sorry peeps.  It's an impossipuzzle.  To see why apply a checker pattern to the squares: 18 black squares but only 16 white squares The two removed squares were both white.  So there are fewer white squares than black ones.  But each domino placed covers exactly one white and one black square.  If you could cover it perfectly with 17 dominoes there would be the same number of black and white squares.  There isn't, so you can't!

Yay! Clickbait for nerds! What's this?  Read on to find out!