Rich of March House

It's not every day you find a 5 inch long beast eating out of the flowers in your garden, but just now we did. Click for bigness.

Someone told me about an interesting "efficiency" change that happened here at work the other day.

We're lucky enough to have a small library on site here, full of books about how to do the things that we have to do, newspapers, journals and such like.  You can borrow a book for a set amount of time and if you keep hold of the book for more than the allowed maximum then someone working in the library used to email you requesting that you return the overdue publication ASAP.

This simple email procedure was changed some months back.  The new procedure entailed the library worker doing these steps:

• Printing off a "Your book is late" standard note from the database of book loans.
• Scanning the printed "Your book is late" note on a flatbed scanner.
• Emailing a PDF version of the printed note to the borrower.

Fortunately, not long after this new improved procedure was introduced it was scrapped when a random microgramme of common sense accidentally drifted into the mind of someone in charge.

All being well we should be moving to a different house soon. We are moving to a house numbered 25, which is pretty good in a mathematical sense because not only is it a square number but it is also the smallest square that can be written as the sum of two other squares (25=16+9, or 5²=4²+3²).

That got me thinking about other house numbers that I have lived in, and what makes them special. A quick bit of research reveals:

• A house where I was born for which I am usure of the number so am unable to comment.
• A house where I spent my first four years. I can't remember this house number either.
• Number 19 where I lived between ages 5-17. 19 is the 8th prime number. It also happens to be the maximum number of 4^th powers needed to sum to any number.
• Then I lived at number 21 briefly when I went off to university. This is the smallest number of distinct squares needed to tile a square.
• After that I lived at number 147 (also while at university). Apart from being the maximum break at snooker, 147 is also the number of 6-sided hexes.
• I left uni and rented at some other house, the number of which escapes me.
• Then I lived at number 47 for a while. This is the largest number of cubes that cannot tile a cube.
• Following that I moved to York for a bit and lived at number 63. This is the number of partially ordered sets of five elements.
• Finally, for now, I live at number 77, which, as everyone knows, is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.

I bet noone else can claim such an interesting list of house numbers to have lived at.

Here's a simple board game a friend and I invented.  I haven't yet gone into production to make myself a millionnaire with this idea.

The game is for two players.  It takes place on a rectangular board of x columns by y rows.  Each player has x counters of a different colour, one of each is placed at the bottom of each of the x columns.

The idea is to get your counters to the tops of the columns.  Moves are made in turn by rolling z dice.  Once you have rolled you can distribute the score across as many or as few of your counters as you like.  For example, if you roll a three you can put all three moves into a single counter to zoom it up a column quickly, or you could move one counter up by two squares and another up by one square, or you could move three counters up by one square each.

For each column, if you get your counter to the top before your opponent then you score a point.  Therefore, in each game there are x possible points that can be scored.  The idea is to gain a larger proportion of the x points than your opponent.

I'm not sure of the optimum tactics of this game but I think they involve abandoning slightly less than half of your counters and putting all your points into the remaining
ones to try and get them all to the top of the board first.

x, y and z can be selected as whatever you like to vary the game a bit.  Again, I'm not sure how this changes the game strategy or theory behind it.