Things 56: Robot Hand, Earth and Moon, Magical Ground Squirrel Puzzle

(Originally sent August 2009)


“Most problems are side effects of solutions to other problems.” – Eskil Steenberg

Once you have built a machine or robot that can do something, the really cool part is you can then see how fast it can do that thing. In the case of this astoundingly dextrous robot hand, the answer is: alarmingly fast.

A simple idea – a picture representing the earth, the moon, and the distance between them, in the correct proportion.

(Click for description and links to bigger versions):

Last Week’s puzzle
Why are ~10% of people left-handed?

Implicitly, the question is really why 10% instead of 50% or 100%, either of which would be intuitively more obvious (although you’d still wonder why it was one out of those two).

A frequently given answer is that in combat there is an advantage to having a handedness that most others don’t have, since you will be practiced at fighting opposite-handers whereas most of the competition will be practiced against fighting same-handers. An increased number of left-handed players succeeding in adversarial sports such as tennis is cited as evidence.

What’s fascinating about this argument is that it manages to sound convincing but it cannot possibly be the whole answer. If there was an advantage to being in the minority, and if that trait is genetic, then we would expect that over evolutionary time-scales a 50/50 split would emerge. (If fewer are left-handed and have a survival advantage by this argument, then more of the next generation will be left-handed, and so on until no advantage remains).

For the theory to work, there would need to be an evolutionary pressure that goes the opposite way, making left-handedness disadvantageous in some way, with the net effect of the two pressures to be a 10% incidence rate.

As it turns out, it seems we don’t have a definitive answer, but surveying the various theories and research presented in this wikipedia article below it seems to be connected to asymmetry in brain development (a deeper question in itself), with cultural effects (such as fighting) giving an additional skew in the short term.

This Week’s puzzle
There’s a very nice puzzle in quantum information theory. This is my attempt to set the same puzzle in less specialist terminology, and although it ends up being quite long, it does involve a magical ground squirrel.

There is an island in the centre of a large lake.

On the island is the entrance to a tunnel that goes deep underground to the imp underground city.

To the North and South of the lake are two evil imp warrior training centres.

To the East and West of the lake are two good imp warrior training centres.

There has recently been an imp general election, and they will either have elected a good leader or an evil one. 1,000 imp warriors will now be allocated a training centre, with exactly 500 allocated to each one. So, if an evil leader has been elected, 500 imp warriors will be assigned to the North training centre, and 500 the South training centre. If a good leader has been elected, 500 imp warriors will be assigned to the West training centre, and 500 to the East training centre.

You are a magical ground squirrel that lives on the island.

A pair of bridges connect the island to the lake shore in opposite directions.

Your magical power is exactly this: you can rotate the pair of bridges so they lie in any direction from the island, so long as they remain directly opposite one another. So you could choose to have one bridge head directly North and one directly South, or one directly North-West and the other directly South-East, and so on. However, you must never use your magic when an imp is on the island or a bridge, as they will notice and put you in their magical animal zoo.

The 1,000 imp warriors are about to be sent out, one each hour, to go to their respective training centres. Imps are highly random creatures, and they also have a pretty amazing sense of direction. They will be coming out in a random order, and they will head along the bridge that most closely matches the direction of their training centre. If the bridges seem to be perpendicular to the direction they want to go (for example, if the bridges lie East and West and the imp wants to go North) then the imp will pick a bridge at random.

Using only your magical ground squirrel powers, what is the best way to work out whether the imps have elected a good or evil leader?

(Note: this is not intended as a lateral thinking puzzle! You just have to decide how to rotate the bridges and interpret the resulting imp behaviour. But I suppose you could try solving it laterally as well. P.S. Imps can cross a bridge in under half an hour).