#techniquest

We stared with a trip to lidl to pick up some bbq stuff. The kids looked super cute pushing their mini trolleys around and only caused a little bit of chaos. Not sure they totally understood the point of shopping and seemed more concerned with who had the most stuff into their trolly, still it was fun.

We had a great bbq, played on the swing and had a little cuddle time before we went to techniquest again. The kids seem to love it there

What a fantastic day with the kids, we went to techniquest (or taco as neco calls it) because ape went there last week with her school. She loved showing us around evewhere, im surprised how much she loved it, she was a proper little leader. Neco had fun too, he started feeling rough after an hour so we had to leave and ape was obliging even though she didnt want to leave. She wanted to go to 'the red McDonald's with gravy' which we deduced was KFC. Neco stuck to me like a limpet because he didnt feel too good and I feed him chips like a chimp. It felt good to comfort him, the way he nestled in for comfort was super cute. Loved being there for him. Big thanks to apey for dunking my chicken in gravy and passing it to me, such a helpful girl. She really tried to help neco feel better too. Oh and I love how disappointed they were that I couldn't sit in the back with them, they really wanted me to, and ape played my 'sun' game with neco to keep him entertained

A bit more Techniquest and Mathamagic cribbing here, although it in turn is based off a much older puzzle.

So you’re probably familar with the Tower of Brahma/Tower of Hanoi puzzle.  You have three pegs, and a set of discs increasing in size on one of the pegs.  In this illustration here, we have four discs:

The goal of this puzzle is to get the stack of four discs from one peg to either of the others, obeying the following rules:

You may only move one disc at a time.

The disc has to go to one of the other two pegs

Bigger discs cannot be placed on top of smaller ones.

And it’s an excellent puzzle, requiring a good deal of strategic thinking and forward planning.  But it’s also a little old hat - the method for finding the solution with the fewest moves (15 for four discs, incidentally) is very well known at this point, and even if you don’t know it, it’s such a famous puzzle that it’d be easy enough to look up.

So my actual puzzle today is going somewhere slightly different:

We’ve split the discs up onto two pegs, so the red (odd) are on one peg and the blue (even) discs are on the other.  Now your goal is swap over the two stacks of discs, following the same three rules as for the regular puzzle.  The least number of moves this puzzle can be solved in is 11 - can you find that solution?

Heading back to Techniquest for this one, although with a couple of differences:

This puzzle is actually based off a game rather than directly a puzzle in itself.

This game isn’t on our exhibition floor, but is part of a special yearly event we run called Mathamagic - for a few weeks every June, we run a special maths-themed event for Key Stage 3 (11-14yo) school groups.  It involves opening up the space on the normally-unused second floor (third floor for Americans / Japanese) of Techniquest, and filling it with extra maths-based puzzles and games.

The game is called Pig, it’s for two or more players, and all you need to play it is a fair six-sided die and some paper and pencils for scoring.

On your turn you roll the die, and if you get any number other than 1, you keep a mental note of it as your score for the turn.  You then have the option to twist or stick - either you can roll the die again, and keep adding to your score for this turn, or you stop rolling the die, add your current turn score onto your total score, and pass the die onto the next player.

Of course, there’s a catch or you’d just choose to twist forever.  The catch is that if you ever roll a 1, you score 0 for the turn, and also pass on the die.  The goal is to be the first player to get their total score to 100 points.

So it’s a game of risk-reward.  Stick too early, and you’re potentially passing up an opportunity to score more points.  Stick too late, and you risk losing too much.  So the puzzle is, when is the optimal time to stick?