Puzzle Night: Nocturnal riddles with friends

The night will be broken into two parts. The first hour will be focused on problems posted in advance on the meetup site. The puzzles are below, along with some questions to ponder while you work on them. The second hour will be broken into 4 rounds of puzzles that will be introduced at the meetup. Come alone or with a group, discussion and help will not be discouraged.

Paper and pencils will be provided. Puzzles will a mixture of logic, math and some riddles. The ones posted here will be more open ended for discussion and the ones featured the night of the meetup will be more traditional riddle and puzzle fair.

Puzzle # 1:

By adding mathematical symbols, can you make each statement true? You cannot add any extra numbers, for example 4 * 1 + 1 + 1 is not a legal move, and cube roots don't work, but square roots are fair game. 6 is done to give you an idea.

0 0 0 = 6

1 1 1 = 6

2 2 2 = 6

3 3 3 = 6

4 4 4 = 6

5 5 5 = 6

6 +6 -6 = 6

7 7 7 = 6

8 8 8 = 6

9 9 9 = 6

Puzzle #2

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?

A varation on a puzzle we had in a previous meetup. Found here: http://www.xkcd.com/blue_eyes.html

Puzzle #3:

Three different numbers are chosen at random, and one is written on each of three slips of paper. The slips are then placed face down on the table. The objective is to choose the slip upon which is written the largest number.

Here are the rules: You can turn over any slip of paper and look at the amount written on it. If for any reason you think this is the largest, you're done; you keep it. Otherwise you discard it and turn over a second slip. Again, if you think this is the one with the biggest number, you keep that one and the game is over. If you don't, you discard that one too. The chance of getting the highest number is one in three. Or is it? Is there a strategy by which you can improve the odds?

Do you have any favorite puzzles? Any websites, books, or radio shows featuring brain teasing math questions?