Trace: • winter2015
This is an old revision of the document!
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)
Questions Asked
| Junming Diao | 1 |
| Jay Brady | 1 |
| Josh Sypherd | 0 |
| Dr. Jeffs | 0 |
| Richard Black | 1 |
| Dr. Warnick | 0 |
| Wu Yifeng | 0 |
| Mitchell Burnett | 1 |