Penn State Math Club March 31 st, 2008

MacArthur Puzzle Directions: Write down the number of the month in which you are born Double it Add 5 Multiply by 50 Add your age Subtract 365

MacArthur Puzzle Proof Let m = month of birth Double it: 2m Add 5: 2m + 5 Multiply by 50: 100m Add age: 100m a Subtract 365: 100m – a Add 115: 100m + a

The Locker Problem As 500 students enter a school, they pass lockers that are numbered from 1 to 500. The first student opens every locker; the second student closes every second locker; the third student changes the position of every third locker (by opening the closed lockers and closing the open lockers); and the fourth student changes the position of every fourth locker. This pattern continues for all 500 students. Which lockers are open after all students enter the school?

The Hat Problem There are 100 people lined up on the steps of a stadium, each on a different step, all looking down toward the field so that they can see everyone in front of them, but no one behind them. Each person will be given either a red or black hat. We do not know the total number of red or black hats. Each person will not be able to see the color of his own hat (or the ones behind him), but will be able to see the colors of all the hats in front of him. Starting in the back, the last person will be asked what color hat he is wearing. If he guesses correctly, he will live; if he guesses incorrectly, he will be shot immediately. The second to last will be asked, and so on, until we reach the person on the bottom step. Each person will be able to hear what all the people behind him say, and will also be able to hear which people behind him were shot.

The Hat Problem Before we begin this process, the 100 people may meet to discuss a strategy. They can plan whatever they want, but once the line-up begins, they may no longer confer. At each person's turn, he may only say "black" or "red," and no other words -- if he says anything else, all 100 people will be executed. He may also not use tone of voice, volume, etc., to convey any meaning -- this will be detected and they will all be shot. What strategy will guarantee saving the maximum number of people? What is this number?

A Familial Math Equation A mother is 21 years older than her son In 6 years, she will be 5 times older than him Where is the father?

A Familial Math Equation Let x = the age of the mother (in years) Let y = the age of the son (in years) x = 21 + y x + 6 = 5(y + 6) Therefore, (21 + y) + 6 = 5(y+6)

A Familial Math Equation y + 27 = 5y y – y = 27 – 30 4y = -3 y = -3/4 Remember that y is expressed in years…

Because everyone needs a little humor in their life – Especially mathematicians

The obvious solution may be correct, but where’s the fun in always being right?

Math Quiz Answers 1) There are 8 apples on the table, you take away 3. How many do you have? 3 – The other 5 are still on the table

Math Quiz Answers 2) There are 10 birds in a field. If 2 are shot, how many are left? 2 – The others have flown away

Math Quiz Answers 3) Take away the first letter, take away the last letter, then take away all the other letters. What do you have left? The mailman

Math Quiz Answers 4) If you have 4 melons in one hand, and 7 apples in the other - What do you have? Big hands

Math Quiz Answers 5) A box holds nine ears of corn. A squirrel carries out three ears a day, but it takes him nine days to carry out all the corn. Why? He carries out one ear of corn in addition to his own two ears

Math Quiz Answers 6) Why do white sheep eat more than black sheep? There are more white sheep than black sheep.

Math Quiz Answers 7) It takes 7 men 2 hours to build a wall. How long does it take 3 men to build the same wall? Why bother? The 7 men have already built it.

Math Quiz Answers 8) I have 2 coins in my hand that add up to 60 cents. One of the coins is not a half dollar. What are the coins? A half dollar and a dime one (the dime) is not a half dollar

Math Quiz Answers 9) "I will bet you $1" said Fred, "that if you give me $2, I will give you $3 in return." "Done," replied Tom. Was he? If Tom gives Fred $2 and Fred does not give $3 back, he loses the bet and $1. Therefore, Tom must give Fred $1.

Math Quiz Answers 10) "How much will one cost?" "25 cents" "How much will fifteen cost?" "50 cents" "OK then, I'll take one hundred sixteen" "Thank you, that will be 75 cents please" What is going on here? A man is buying house digit numbers

Math Quiz Answers 11) A Hammer and a Nail cost $31. If the hammer cost $30 more than the nail, what is the cost of each? The hammer is $30.50, the nail is $0.50

Math Quiz Answers 12) A man wanted to plant 4 trees, but all 4 had to be equal distances from each other. How did he do it?

Math Quiz Answers 13) A fisherman was asked the length of the fish he had caught. He said "it is 30 cms plus half its length.“ How long was the fish? 60 cms

Math Quiz Answers 14) What comes next in the following sequence ? 1, 4, 5, 6, 7, 9, 11, – the next number spelled without a t

Math Quiz Answers 15) In a scientific context, what could the following phrase mean? “How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics…” π = …