Ten Problems

Here’s a puzzle I heard from a friend yesterday. After a long drought devoid of any updates, I thought I’d post this one.

Five pirates have a chest of 100 gold coins to be divided amongst them. The pirates (A, B, C, D, E), are ranked by seniority, where A is the most senior pirate. The rules are these:

1. Pirate A presents a scheme of dividing the coins to the other pirates, who then vote on this scheme. If there is a majority (Pirate A also participates in the vote), then the coins are divided. If no majority is reached, Pirate A walks the plank and we proceed to the next step.

2. Pirate B presents a scheme, and have the remaining pirates vote on it. If there is a majority, then the coins are divided. If there is a tie, Pirate B have the final say. If a majority votes against the scheme, Pirate B walks the plank and we proceed to Pirate C.

3. Same as Step 1, except with only 3 pirates left. If no consensus is reached, we continue until there is one pirate left.

The question is, how should Pirate A divide the coins such that he gets as many coins as possible, assuming all pirates are extremely smart and knows the optimal strategy?

I have 61 identical looking coins in my pocket. Two of the coins are counterfeit, and the other 59 are solid gold. The only difference between the counterfeit and the gold coins is their weight, but we don’t know which one is heavier. How can I use a balance to find out whether a counterfeit coins or a gold coin is heavier?

Solution:

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There are many more ways to solve this problem. Can you figure them out?

Generalizing the problem to a total of 6k+1 coins (k a positive integer) including two counterfeits, can you find a general method?

Here’s a famous one:

I start with the letter E.
I end with the letter E.
I usually contain only one letter
Yet I am not the letter E!
What am I?

Which common 9-letter English word remains an existing word each time you remove a letter from it until it is a one-letter word?

What am I?

1. I’m always excited
2. I tell people where they are
3. I’m always with numbers
4. I’m rich
5. I’m a part of a whole
6. I’m edgy
7. I’m curvy
8. I’m a star!
9. I tend not to stand up straight

Here’s a classic.

A man is travelling with a tiger, a goat, and a cabbage. He needs to cross a river and has only a small boat. It is so small that he can only carry one belonging at a time.

If the tiger eats the goat and the goat eats the cabbage if left unattended, how can the man cross the river with all his belongings intact?

As I was going to St. Ives,
I met a man with seven wives.

Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits.

Kits, cats, sacks, wives,
How many are going to St. Ives?

A bottle containing a coin is sealed with a cork at the bottleneck. How can you take out the coin without taking out the cork or breaking the bottle?

Mrs. Kedringham was a riddle-obsessed teacher. Every day, she would put a riddle on the board, and whoever solved it would have a reward. The smart student Jennifer almost always solved them, but on this occasion she was stuck. Can you help her?

I drink the blood of the Earth,
And the trees fear my roar,
Yet a man may hold me in his hands,
I can even be bought at a store.

Solution

How does ??

Update: Solutions are posted!

This is a classic that many of you have doubtless seen before.

Link

What happened to the missing square?

Image source: Wikipedia

Update: Solutions are posted!

Certain bacteria reproduce and grow twofold in number every minute. If at 12:00 noon one bacterium was introduced to a container and at 1:00 PM the container was full, when was the container half full?

Solution

Draw the hopscotch figure, like the one below, without lifting the pencil.

Solution

Once again, take a chess knight and place it anywhere on an 8 by 8 chess board. Find the longest path the knight can take without intersecting itself.

Solution

Start with a knight on any square on an 8 by 8 chess board. Keeping in mind the way a chess knight moves (two squares in any non-vertical direction and then one square in the perpendicular), find a series of moves such that the knight travels through every square only once.

Solution