The Magic Square

This is one I come back to when I'm bored and all I have is pen and paper.  I also read in a biography of Benjamin Franklin that he used to do this when he was stuck in boring meetings.  Construct a 3x3 grid of numbers, using numbers 1 through 9, and arrange the numbers in the square such that every row, column, and diagonal (diagonals through the center) adds up to 15. 


Too easy?  Now construct a 4x4 grid made out of numbers 1 through 16, such that every row, column, and diagonal adds up to 34.  This one is killing me because I figured it out once, but can't seem to rediscover the solution.  There are ways to do this for grids 5x5, 6x6, and up, though they no doubt get very difficult.

No Riddle This Week

I can't think of any and I'm too busy with work, sorry everybody. 

4=5

The other day, someone in our creative services department tried convincing me that 4=5.  He offered a convincing proof, which is displayed below.  But what is wrong with it? 

Pirates, Part 2

Again, taken from folj.com. 

The five pirates mentioned previously are joined by a sixth, then plunder a ship with only one gold coin.


After venting some of their frustration by killing all on board the ship, they now need to divvy up the one coin. They are so angry, they now value in priority order:

1. Their lives
2. Getting money
3. Seeing other pirates die.


So if given the choice between two outcomes, in which they get the same amount of money, they'd choose the outcome where they get to see more of the other pirates die.


How can the captain save his skin?

The Blind Date Bachelor

(Modified from a puzzle about a sultan and his harem I heard from Jon Huang.) The Blind Date Bachelor is the newest dating show, in which where there is 1 bachelor and 4 contestants trying to win his heart. He will meet each contestant for the first time on a blind date. At the end of the date, he must choose whether to marry her or never see her again. If he marries her, the game is over. If he rejects her, he is set up on a date with the next contestant and repeats the process. If he rejects the first 3, he marries the last one automatically. He is able to compare and rank contestants that he has already met, but will not know for sure who he likes best until he has met them all. It's very important that he marry the best one, or he will spend the rest of his life wondering what could have been. What strategy will maximize his chances of finding the best mate-for-life?

3 Bonus Questions: What is the probability of winning using the best strategy?  What if there are 5 contestants, not 4?  And finally, what if there are n contestants? 

Pirates

I've seen this one before and haven't solved it.  Go ahead and comment answers in the blog, but not on Buzz or else  people will see them.  I quote this one from folj.com, but I've seen it before in other places as well. 

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.
If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?

Dots and Lines

This is a very old one, and many of you may have seen it before.  I try to avoid posting puzzles with outside-the-box solutions, but I made an exception for this one.  Using 4 straight, connected lines, connect all 9 dots.