Question: A smart landscaper is given the task of placing 4 trees so that they are all the same distant away from each other.
How does he do this?
Answer: He puts three trees into a triangle then one on a hill in the middle (this forms a tetrahedron).
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.
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.
Question: Tom wants to send Sally an expensive ring through the mail because they live thousands of miles apart. The only problem is that everything sent through the mail is stolen unless there is a lock put on it. Both Tom and Sally have plenty of locks and keys but they don't have any of the same locks or keys.
How can Tom send Sally the ring without it getting stolen?
Answer: Tom puts one of his locks on the box with the ring in it. When Sally gets it she puts one of her own locks on the box and sends it back to Tom. Finally Tom takes his lock off of the box and sends it back to Sally who can then unlock her own lock and retrieve the ring.
Question: You are playing a game of dodge ball with two other people, John and Tom. You're standing in a triangle and you all take turns throwing at one of the others of your choosing until there is only one person remaining. You have a 30 percent chance of hitting someone you aim at, John has a 50 percent chance, and Tom a 100 percent change (he never misses). If you hit somebody they are out and no longer get a turn.
If the order of throwing is you, John, then Tom; what should you do to have the best chance of winning?
Answer: Miss the first time on purpose.
If you try to hit John and do. Then Tom goes next and he will hit you and you will lose for sure. If you aim at Tom and hit him then John will go for you. If you miss on your first turn John will go for Tom for sure because he is a stronger player. If he hits him then it's just you and John, but you are going first. If he misses him then Tom will hit John and it will be just you and Tom, but again in this case you are going first.
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