Tag Archives: games

London MathsJam February Recap

Here’s a rough summary of February’s London MathsJam. There seemed to be some loose themes, but sadly no pancakes (it was on Shrove Tuesday). Peter Rowlett briefly visited, but left before most people turned up and the action started (the official MathsJam start time of 7pm is also the start of off-peak travel on the tube, so people tend to arrive later). We had about ten people in all, down from thirty-odd at January’s, when we took over the whole upstairs of the pub. There’s been a good mix of people in various walks of life, though most (but not all) had (or are doing) maths or computer science degrees: but everyone likes puzzles and games. This isn’t a full round-up: people sometimes split off into smaller groups, so it’s hard to keep track of everything, and there’s lots of chit-chat along the way that I haven’t documented.

♥ Someone autobiographically wondered what the chances of having two fire alarms in a day is.

♣ People were concerned when I brought out this noughts and crosses tiling puzzle (Think Tac Toe from this puzzle series), worrying at first it might be a physical copy of game itself:

The only solution anyone found wasn’t one of the four given on the back of the box:

Though it seems an unlikely to occur in a real game, it is a valid game position, so the solution is valid.

♣ Because noughts and crosses was universally unloved, we suggested replacements: Sim was explained, and 3D tic-tac-toe was played (on a 4×4×4 grid).

◊ Can you fit five rectangles together to form a square, where the rectangle side-lengths are each of the whole numbers 1 to 10? How many ways are there?

♦ Can you fit all twelve pentominoes, and an additional 2×2 square into: an 8×8 square; or into a 4×16 rectangle. We didn’t have time to try this one, or have any pentominoes handy.

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Tie Fighters

Noughts and crosses (tic-tac-toe) is quite a boring game. The two main reasons for this are:

  1. Most games end in a draw or tie.
  2. The optimal strategy is too obvious (the first player wants to start in the middle).
With an ulterior mathematical motive in mind, I’d like to introduce you to two games that avoid the first complaint. Whether they address the second is up to you: I’d argue that only Game B, called Sim, does.
Game A 
Let’s call the game triangle-tac-toe. Draw a grid in the shape of a right-angled isosceles triangle whose sides are five squares across (giving 15 squares in total). A board-drawing hint: draw five rectangles.
Starting grid
Take turns to add noughts or crosses as in traditional tic-tac-toe. A player wins when three of their marks form the corners of a right-angled isosceles triangle of any size in the same orientation as the board (the corners may be touching or spread out).
Some of the possible ways for Crosses to win.
Game B (Sim)
Draw six points in a hexagonal arrangement. Optionally, lightly join each possible pair of points (a total of 15 lines) with dotted lines—don’t worry whether three cross lines in the middle or not, but double check that each point has five lines coming out of it.
Sim starting layout
Players pick their favourite colours (we’ll use the traditional Red and Blue), and take turns drawing a straight line in their chosen hue between two points (that haven’t already been connected). A player loses if they form a triangle of their colour between any three of the hexagon’s vertices.
End of a sample game—Red loses due to the highlighted triangle
Animation of the sample game above (click if not playing)

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