Sometimes I start newcomers to MathsJam on timing puzzles. Here are five classics in increasing order of difficulty and implausibility, each with a distinct flavour. The first is distinctly steaky…
1. Some friends are coming over for a steak dinner. You want to cook three steaks as quickly as possible, but your grill pan only holds two at a time. Each steak must be cooked for five minutes on each side. What is the fastest you can have all three ready? Show that you can’t do any better.
Alas, when this precise situation once arose with my family at home (who says puzzles are never useful?), I was unable to convince my father not to cook the steaks in the obvious order. But at least that meant I got my steak sooner.
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.