Brain Teasers and Puzzles

Island of Blue Eyes

There is an island known for its people with blue eyes, yet there is at least one green-eyed person on the island. No one knows the color of their own eyes, as there are no reflective surfaces on the island and discussion of eye color is forbidden, but they can see everyone else’s eye color. If any islander were to come to know that they do not have blue eyes, they would leave the island in shame before the next sunrise.

One day, an outsider visits the island and remarked how there was at least one islander with green eyes. Within the day, every islander had heard and understood this new information.

Assuming departures from the island are noticed by everyone by the next day, and assuming each islander is highly logical and is able to keep track of all other islanders’ eye colors and actions – what happens to the islanders and does it depend on the number of green-eyed islanders?

This is a classic logic puzzle, also known under a different story (but same core logic) as Josephine’s Problem.

Brain Teasers and Puzzles

Wrongly Labeled Boxes

You run a small business that sells and ships widgets. Today, you received three orders: one customer bought two blue widgets, one bought two red widgets, and one bought one red and one blue widget. Each widget is carefully packaged without any indication of the color inside, and then you pack the each order of two packaged widgets into boxes, tape them up, and stick shipping labels on them using your digital label printer.

However, there was a glitch with the software, and it labeled all three boxes incorrectly. You need to figure out the correct labels, but you forgot which box contained which widgets.

What is the fewest number of widgets you have to inspect before you know how to correctly label all the boxes, and which do you inspect?

This was a popular brainteaser in some engineering interviews a while back, often using “apples” and “oranges” instead of red and blue widgets.

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