Start both hourglasses then when the 11 minute hourglass has finished immediately flip it again. When the 13 minute hourglass runs out the 11 minute hourglass will have 9 minutes left, so flip it and it will last another 2 minutes, 13 minutes + 2 minutes = 15 minutes.
A hobo picks up cigarette butts from the ground and can make a cigarette with 4 butts. If he finds 16 cigarette butts, how many cigarettes can he make?
An ant gets onto one end of a tight rope that is 1 meter long. The ant is traveling at 1 centimeter per second, but the entire rope is being stretched an extra 1 meter (1,000 centimeters) a second (it can be stretched forever).
Will the ant ever reach the other end of the rope?
Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation.
Conditions: Each must be used exactly once and no other numbers or symbols can be used.
There are two planes. One is going from Los Angeles to Japan at a speed of 600 MPH. The other is traveling from Japan to Los Angeles at a speed of 500 MPH.
When the planes meet which one will be closer to Japan?
Mike 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?
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.
7.5 degrees.
The minute hand is pointing directly at the '3'. The hour hand is 1/4 of the way between the '3' and '4'. Since there are 12 numbers the angle between each number is 30 degrees. So the angle between the hands are 30 degrees * 1/4 = 7.5 degrees.
5 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?
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.
Four people need to cross a bridge in 17 minutes in the middle of the night. The bridge can only hold two or less people at any time and they only have one flashlight so they must travel together (or alone). The flashlight can only travel with a person so every time it crosses the bridge it must be carried back. Tom can cross in 1 minute, John can cross in 2 minutes, Sally can cross in 5 minutes, and Connor can cross in 10 minutes. If two people cross together they go as fast as the slower person.How can they cross the bridge in 17 minutes or less?
First Tom and John will cross (2 minutes). Then Tom will bring the flashlight back (1 minute). Next Sally and Connor will cross (10 minutes). Then John will bring the flashlight back (2 minutes). Finally John and Tom will cross (2 minutes). 2 + 1 + 10 + 2 + 2 = 17 minutes.
In an apartment complex in New York there are one hundred married couples. When one of the husbands cheats on his wife with one of the other wives, his wife has no idea. With the large amount of gossip in the complex, all of the other wives know he is cheating. If a wife finds out that her husband is cheating on her, she kills him the following morning. Someone anonymously sends an email to all of the wives in the building saying that at least 1 man is cheating on his wife in the building.
How many husbands will be killed and how long will it take?
All of the men (n) who are cheating will be killed and it will take one less than the number of cheating men nights (n-1) for their wives to discover this.
If one man was cheating, and that woman hadn't have heard of any other infidelity she would know it was her husband that was cheating. If there was two men cheating, both of their wives would think that since they have only heard of one man cheating he should die the next morning. If he doesn't die, she knows her husband must also be cheating and that's why the other husband didn't die. Following this logic, you can know that all of the men will die after one less night than there is cheating men.
There is a 5 gallon and a 3 gallon bottle. You also have a hose with unlimited water. How are you gonna make the 5 gallon have 4 gallons using your items?
(You don't know the exact dimensions of a gallon)
You fill the five gallon up and pour it into the 3 gallon. The dump the 3 gallon out and pour what was left in the 5 gallon into the 3 gallon so that you have 2 gallons in the 3 gallon. Then fill the 5 gallon up and pour it into the 3 gallon to fill it up. Now you have 4 gallons in the 5 gallons.
You have been given the task of transporting 3,000 apples 1,000 miles from Apple-York to Strawberry-Ville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Strawberry-Ville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Apple-York).
What is highest number of apples you can get to Strawberry-Ville?
833 apples.
How to solve:
You need to make 3 trips of 1,000 apples - 333 miles. You will be left with 2,001 apples and 667 miles to go.
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).
Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Strawberry-ville.
Given two 2s, "plus" can be changed to "times" without changing the results: 2 + 2= 2 x 2.
The solution with three numbers is easy too: 1 + 2 + 3= 1 x 2 x 3.
Now find the answer for 4 numbers and for 5 numbers.
For 4 numbers:
1 + 1 + 2 + 4= 1 x 1 x 2 x 4.
For 5 numbers:
1 + 1 + 1 + 2 + 5= 1 x 1 x 1 x 2 x 4
1 + 1 + 1 + 3 + 3= 1 x 1 x 1 x 2 x 4
1 + 1 +2 + 2 + 2= 1 x 1 x 2 x 2 x 2
I have a clock in my house, on the wall.
On a summer's day I forgot to wind it and it stopped. Then I went to visit a friend who had a watch that was always right on time. After I stayed for a bit, I went home, made a simple alteration and set the clock just right.
Now how did I do this when I had no watch on me to tell how long it took me to come back from my friend's place?
Before I left, I wound the wall clock. Upon my return, the amount of change that I could see in the clock is how long it took to go to my friends place and come back, adding to that the time I spent there, which I know because the clock at my friend's place is accurate.
Subtracting the time of the visit from the time I was absent from my house, and dividing by 2, I obtained the time it took me to return home. I added this time to what my friend watch showed when I left, and set the sum on my wall clock.
David was known as being lazy. He agreed to work on a job for his brother-in-law for thirty hours at eight dollars an hour, on the condition that he would forfeit ten dollars per hour for every hour that he idled. At the end of the thirty hours David wasn't owed any money and didn't owe his brother-in-law any money either. How many hours did Larry work and how many hours did he idle?
Lazy David worked 16-2/3 hours and idled 13-1/3 hours. 16 and 2/3 hours, at $8.00 an hour amounts to the same amount as 13 and 1/3 hours at $10.00 per hour.
Twelve flags stand equidistant along the track at the stadium. The runners start at the first flag. A runner reaches the eighth flag 8 seconds after he starts. If he runs at an even speed, how many seconds does he need altogether to reach the twelfth flag?
There are seven distances from the first flag tot the eighth, and 11 from the first to the twelfth. He runs each distance in 8/7 seconds; therefore, 11 distances take
88/7= 12 4/7 seconds.
Walking home one day, you take a short cut along the train tracks. The tracks cross a narrow bridge over a deep gorge. At the point you are 3/8 of the way across the bridge, you hear the train whistle somewhere behind you. You charge across the bridge, and jump off the track as the train is about to run you down. As it happens, if you had gone the other way, you would have reached safety just before being run over as well. If you can run ten miles per hour, how fast is the train moving?
The train is moving at 40 miles per hour.
if there was a dog going towards the train while you go away from it as the whistle blows, he will reach his point when you are 3/4 (6/8) of the way on the bridge, the train will have just reached it. So for the train to cross the bridge at a rate four times yours it will have to be moving 4 times as fast.
Joe has ten coins totaling $1.19. From these coins, he cannot make exact change for a dollar, half-dollar, quarter, dime, or nickel.
What are the coins?
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