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Question: There is a story that a man and not a man
Saw and did not see a bird and not a bird
Perched on a branch and not a branch
And hit him and did not hit him with a rock and not a rock.
[How is this possible?]
Answer: A eunuch who did not see well saw a bat perched on a reed and threw a pumice stone at him which missed.
Question: You have been given the task of transporting 3,000 apples 1,000 miles from Appleland to Bananaville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Bananaville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Appleland).
What is highest number of apples you can get to Bananaville?
Answer: 833 apples.
Step one: First you want to make 3 trips of 1,000 apples 333 miles. You will be left with 2,001 apples and 667 miles to go.
Step two: Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).
Step three: Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Bananaville.
By Jane Austen
Question: When my first is a task to a young girl of spirit,
And my second confines her to finish the piece,
How hard is her fate! But how great is her merit
If by taking my whole she effects her release!
Question: A fast food restaurant sells chicken in orders of 6, 9, and 20.
What is the largest number of pieces of chicken you cannot order from this restaurant?
After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).
Question: My first is often at the front door.
My second is found in the cereal family.
My third is what most people want.
My whole is one of the united states.
What am I?
Answer: Matrimony (mat rye money). Which is certainly a united state!
Question: You have two coconuts and you want to find out how high they can be dropped from a 100 story building before they break. But you only have $1.40 and the elevator costs a dime each time you ride it up (it's free for rides down).
How can you drop the coconuts to guarantee you will find the lowest floor they will break at, while starting and ending at floor 1?
Note: They break when dropped from the same height and they don't weaken from getting dropped.
Answer: You could drop it at floor 1 first (because you start at floor 1). Then you would go to the floors: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, and 100. Whatever floor your first coconut breaks at, go to the floor above the last floor the coconut survived and drop the second coconut from this floor. Then go up by one floor until the second coconut breaks and that is the lowest floor it will break at.
Question: Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.
Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.
What are the numbers?
Answer: The numbers are 3 and 4.
Since Sam knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Pete (who knows x*y) knew that Sam didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Pete doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2). At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.
John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
Answer: 301 eggs. The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.
Question: Five pirates are parting ways after finding a treasure of 100 pieces of gold. The pirates decide to split it based on a vote. Each pirate, from oldest to youngest, gets to propose a plan on how to split the gold.
If at least 50 percent of the other remaining pirates agree on the plan, that is how they will split the gold. If less than 50 percent of the pirates agree, the pirate who came up with the plan will be thrown overboard. Each pirate is smart, greedy, and wants to throw as many others overboard as possible without reducing the amount of gold they get.
What plan can the first (oldest) pirate propose to live and get as much gold as possible?
Answer: He can propose a plan that he gets 98 pieces of gold, the 3rd pirate gets 1 piece, and the 5th pirate gets 1 as well.
If there were just 2 pirates the younger pirate would definitely deny the plan so he could get all of the gold.
If there were 3 pirates the first pirate can offer the second pirate 1 piece of gold and take the rest himself because the second pirate wouldn't get anything if he has to propose a plan himself.
If there were 4 pirates the first pirate could take 99 for himself and offer 1 to the youngest pirate. They would both agree. If the youngest disagrees then he won't get any gold in the next plan.
So when there are 5 pirates it is in the interest of the 3rd and 5th pirate to accept 1 piece, because if they don't they won't get anything in the next plan.
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