Radio Astronomy Systems Research Group

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 2^nd locker. Then you go back and visit every 3^rd locker: if it is open you close it, if it is closed you open it. You continue this process toggling every n^th locker. On your final pass, n = 100. After all of this, how many lockers will be left open? (Bonus: which lockers are they?) ¹⁾

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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⁾

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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⁾

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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⁾

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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⁾

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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⁾

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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⁾

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