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:

Show ▼

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?

Change one letter at a time to make Time out of Dell, but they have to be real words.

Dell

Time

Melissa sat in the office of Detective Sing.
“I met a man yesterday,” she said. “He’s trying to raise funds for Kids with Cancer by driving non-stop around Australia. He says he did it last year; drove to all the Australian Capitals in two and a half weeks. He says that he wants to try and break that record this year, and that if he does, the Australian Government will give a $10,000 donation to the charity. The only problem is that he needs funds to pay for the car, petrol and food. He’s asked me for an initial donation of $2,000. What should I do? Should I give it to him?”

Detective Sing paused for a moment. “You could give him the money,” he said. “But I don’t think it will help the charity.”

Why?

The Optimist and the Pessimist were arguing whether the wine barrel in front of them was half full or half empty. Then the Pragmatist came and showed them without measuring anything or removing any wine. How did he do it?

Three Kings agreed to a duel to settle an argument. The rules:Each king brings a gun with only one bullet. Then they will decide on a certain order to shoot.

We know that King #1 and King #2 are masters in shooting who never miss.We also know that King #3 is a very poor shooter and never hits the target.

Who is the most likely to survive?

Deborah, Samantha, Eli and Aaron all went to the mall. When they all were hungry, they went to the food court. Their choices were: Chinese, Italian, Mexican, and Southern. However, they all went together to get their food. What food did they order and in what order did they get their food?

1. Eli loves sushi.

2. Samantha went before Aaron.

3. Aaron likes Southern and Mexican, and he went second.

4. Deborah loves pinto’s and cheese.

5. Eli went right after Aaron.

6. Samantha went before Deborah, and she loves Chicken Alfredo.

Solution

You have 101 coins, 50 of which are and the rest are . coin weights 1g more than coin. You have a balance to calculate the difference of two sides in gram. If you have to choose one coin from this 101 coins, how can you know whether it’s or ? How do you do this using the balance the least number of times?

There are 7 people and 1 animal, Allen and his sons John and Chan, Percy and his sons Thomas and Donald, a hunter and a wolf on one side of the river. There is a boat which can carry 2 people at any time. Only Allen, Percy and the hunter can row the boat. How do they all cross the river without being killed if
1. The wolf will eat everyone if the hunter is not there.
2. Allen will eat Thomas and Donald if Percy is not there.
3. Percy will eat John and Chan if Allen is not there.

Here’s a fun game for two. The first person says a number between 1 and 10. Then the other will say a number that is at least 1 higher and at most 10 higher than the previous number. They go back and forth until one says 50 and wins. What’s the winning strategy for the person who starts?

A large toy bag contains 8 yellow Lego pieces, 7 red pieces, and 5 black pieces. Without taking a peek in the bag, Igor takes out N marbles at one. If he is to be sure that he will have 4 Legos of one color and 3 of another left in the bag, what is largest possible value of N?

Update: Solutions are posted!

Here’s a puzzle involving a fair amount of analysis and calculation, but I rather enjoyed doing it.

Allen and Percy were helping their good-tempered teacher Ms. Letourneau move to a new house. There were 16 small boxes and 10 large boxes. Allen takes 2 minutes to move each small box and 6 minutes to move each large box while Percy takes 3 minutes to move each small box and 5 minutes to move each large box. They start moving after school at 4:00pm, and spent 30 minutes to discuss the best strategy to spend the least time moving boxes before getting to work. When is the earliest time they could finish?

Note: They can’t hand off the boxes in the middle of the trip.

Update: Solutions are posted!

Tinman was in quite a pickle. He was choosing a vehicle that he had to drive for the next 7 years, and he had to make the best decision possible. He had only five choices to choose from, and the choices each had different qualities that made them better or worse.

If the third choice was worse than the first choice and the second choice as good as the fifth, but the fifth choice was only as good as the worst choice leaving the fourth choice a little better than the third but not as good as the first, and the second was the worst choice to go with, which choice should Tinman go with if he wanted the best vehicle?

Solution

Five avid scrapbookers from Forest Hill get together every weekend to swap page ideas and discuss the progress that they have made on their scrapbooks during the week. Each scrapbooker lives on a different street, scrapbooks on a different night of the week and completed a different number of pages . Using the clues below, determine the first and last names of each scrapbooker, what street they live on, on which day they scrapbook and how many pages they have completed this week.

1. Gordon finished one less page than the person who lives on Oak, but he finished 2 more pages than the person whose last name is Black.
2. The girl who lives on Oak finished 4 pages.
3. The person whose last name is Green scrapbooks on Thursdays.
4. One person finished 2 pages on Monday.
5. The person who scrapbooks on Tuesdays lives on Pine.
6. Gordon, whose last name isn’t Green, doesn’t live on Evergreen.
7. Mr. White doesn’t scrapbook on Tuesdays.
8. Barbara doesn’t live on Elm Street.
9. The person who lives on Pine did 5 pages, but not on Thursday.
10. Hank lives on Maple, but he doesn’t scrapbook on Wednesdays.
11. Jason scrapbooks on Fridays.
12. The five friends are, in no particular order, Alicia Brown, the person who lives on Maple, the person whose last names is Gray, the person who scrapbooks on Thursdays, and the guy who finished one page.

Solution

There are two tribes, X and Y, in a jungle such that people belonging to tribe X always speak the truth while those in tribe Y always lie.

Suppose you come across 4 such people A, B, C, D:

A B C D

A says: “B is in tribe Y.”
B says: “C is in tribe Y.”
C says: “D is in tribe Y.”
D says: “A will say that C is in tribe Y.”

If there are two people from each tribe, can you deduce who is from which tribe?

Update: Solutions are posted!