## Blue Eyes – a logic puzzle explained

After Tim Harford Tweeted the link to it, I spent a fair bit of time yesterday wrestling with what XKCD reckon to be

## The Hardest Logic Puzzle in the World

Here’s how it runs:

‘A group of people with assorted eye colors live on an island. They are all perfect logicians — if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let’s say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

“I can see someone who has blue eyes.”

Who leaves the island, and on what night?’

Now, it’s possible to Google the answer but I thought it would be interesting the explain how I worked it out.

## Putting the rhythm into algorithm

Recently I’ve been doing some work with Mudlark on a data vizualisation project. Matt Watkins, their lead technologist, suggested that I might like to subscribe to Flowing Data, a daily newsletter with illustrations of different data viz work.

It’s well worth subscribing to. My favourite recent post had a link to the video below which demonstrates the Bubble Sort algorithm by means of Hungarian Folk Dance.

This was created at Sapientia University in Tirgu Mures (Marosv?s?rhely), Romania. They have their own YouTube channel as well as Facebook page. And really, what’s not to like?

## Staring down the wrong end of the telescope

After writing about how many Panini stickers collectors should expect to buy to fill a book I’ve had a fair few comments about it. Greg Newman brought John Crace’s article in The Guardian to my attention where he talks about “the four-yearly great Panini conspiracy theory.” The conspiracy being that Panini don’t distribute the stickers evenly, so you have to buy even more of them to complete your set.

As evidence, he cites Chris Taylor, whose “album is now about two-thirds full and I’ve already ended up with a whole load of Lee Young-Pyos, Hameur Bouazzas and Vince Grellas“. He then compares the fact that he has never even seen a Thierre Henri, whereas Chris has got six. ?hich is an opening for swapsies if I ever heard one.

## Sigh Whitehouse

Will Hutton makes some interesting points about class, and why it still matters, in a recent Observer piece.? But he’s also made a rather startling mistakes in his maths.? He states that

The good luck of being born into the right family is profound. Two American researchers, Betty Hart and Todd Risley, show how children from professional families hear on average 2,153 words per hour compared with 616 words per hour for kids in welfare families, so that by the age of three, there is a 30 million word gap between the vocabularies of children of families on welfare and those of professional families.

A 30 million word gap in vocabulary?? Surely just reading it back would tell you that there is something wrong in that statement.? It looks as though Will has mistaken occurrence for uniqueness.?