Eye colour riddle

23 May 2019

Eye colour riddle

A long time ago on an island far away lived a tribe who were happily isolated from the rest of the world. In fact the had just two rules for the island:

1. No one is allowed to come on to the island
2. If you learn the colour of your eyes, then you MUST permanently leave the island when it next reaches 2pm

Fortunately there are no reflective surfaces on the island, and no one would ever tell someone their eye colour.

As it happens, a lonely explorer sails near the island, she is forbidden to enter but sets up her mooring along the coast and begins to trade with the islanders. After several weeks they are good friends but she decides to return home and makes a short speech at midday to everyone as they line the coast.

She say to the islanders, ‘Thank you for trading with me, you are wonderful people, and I am homesick to see people with blue eyes this far from my home.’

Turns out that there were 5 people on the island with blue eyes, so everyone already knew that there were blue eyes on the island. Were there any repercussions from the traveller’s speech?

Hint below

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Think about what would have happened if only 1 or two people had blues eyes.

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Solution below

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Solution:

• If there was only one person with blue eyes then they would have left at 2pm, because they had never seen blue eyes and therefore they would learn that they have blue eyes
• If there were two people, then no one would leave at 2pm, because each blue eye person would be expecting the person to leave, since they don’t leave then the two people on the island that can only see one pair of blue eyes would then learn that they have blue eyes, and both would leave at 2pm the following day.
• If there were three people then no one would leave on the first two days, so the three people who only see two pairs of blue eyes would leave on the 3rd day
• The pattern can be extrapolated, so 5 people would mean that the 5 blue eyed people would leave on the 5th day.