Trace: • winter2015
Table of Contents
Lockers
You come upon a row of 100 closed lockers. Starting with locker number 1, you open every locker. Then you go back and open every 2nd locker. Then you go back and visit every 3rd locker: if it is open you close it, if it is closed you open it. You continue this process toggling every nth locker. On your final pass, n = 100. After all of this, how many lockers will be left open? (Bonus: which lockers are they?) 1)
Broken Clock
There is a worker in a factory that works 8 hours a day for $6 per hour. There is only one clock in the building, and he isn't sure that it is accurate. He finds out that the hour and minute hand cross every 69 minutes. How much money is he losing or gaining if he uses this clock to time his 8 hour day? 2)
McNugget Numbers
At McDonalds, you can purchase McNuggets in boxes of 6, 9 and 20. What is the largest number of McNuggets that you cannot purchase by some combination of these boxes?3)
Black Cards
There are three piles of playing cards in front of you. Each pile has 2 cards. One pile has two black cards, one has two red cards, and one has one black and one red card. You choose one pile at random. You look at the top card, and see that it is black. What is the probability that the other card on the bottom of your pile is also black? 4)
Ants on a log
There is a 100m long log. On this log, there are 1000 ants randomly placed. The ants all travel at 1m/s either left or right, but their direction is random. If two ants touch, they will both change their direction. What is the average time before all of the ants walk off the end of the log? 5)
Breakfast
Two fathers and two sons are eating breakfast. They eat a total of three eggs, but each person eats one egg. How can this be? 6)
Dots and Lines
How can you arrange 9 dots so that you can draw 10 lines that each touch at least three dots? The lines can cross, but two lines cannot be on top of each other. 7)
Password
A man worked for a high-security institution, and one day he went in to work only to find that he could not log in to his computer terminal. His password wouldn't work. Then he remembered that the passwords are reset every month for security purposes. So he went to his boss and they had this conversation: Man-“Hey boss, my password is out of date.” Boss-“Yes, that's right. The password is different, but if you listen carefully you should be able to figure out the new one: It has the same amount of letters as your old password, but only four of the letters are the same.” Man: “Thanks boss.” With that, he went and correctly logged into his station. What was the new password? 8)
Bricks
A man is being interviewed for a construction job. The boss brings him out to the construction site where they are building a large brick building. To test the man's cleverness, the boss hands him a ruler a asks the man to tell him the length of the diagonal of the bricks they are using. Using only the bricks laying on the ground and his ruler, how can the man find the length of the diagonal of a brick without using any calculations? (The diagonal of the brick is shown in red)9)
Bridge
Repeat quetion. See The Bridge Crossing 10)
Diophantus
The Greek Diophantus is sometimes called the father of algebra. A puzzle was written about him by Metrodorus:
'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.' W
How old was Diophantus when he died? 11)
One Family, One Boy
Suppose a group of Chinese families try to change the usual “one family, one child” policy. The want to make it so that each family has one boy. Under the new policy, if the first child is a boy, that will be the family's only child. If they have a girl first, they can have another child. If the second child is a boy, they can not have any more children. This way, each family will continue having children until they get a boy, then they must have no more children. If this new policy is put in place, what will be the distribution of boys and girls in China after many years? 12)
Questions Asked
| Junming Diao | 3 |
| Jay Brady | 2 |
| Josh Sypherd | 1 |
| Dr. Jeffs | 0 |
| Richard Black | 1 |
| Dr. Warnick | 2 |
| Wu Yifeng | 1 |
| Mitchell Burnett | 2 |