Radio Astronomy Systems Research Group

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===== The Fox and the Rabbit =====
In the forest, there is a meadow. A fox and a rabbit each take 10 seconds to cross this meadow. One day, they both cross this meadow. Their arrival time is uniformly distributed from 4:00 to 4:01 pm. If the fox and the rabbit happen to be in the meadow at the same time, the fox will eat the rabbit. What is the probability that the rabbit survives?((Josh Sypherd, Jan. 8))

[[wiki:donuts:winter2014:foxrabbit|answer]]

===== Wolf and a Lake ====
One day, you are swimming in the middle of a perfectly circular lake. While you are swimming, a wolf wanders up to the edge of the lake. You know this wolf can run 4 times faster than you can swim, and he always runs toward the point on the edge of the lake closest to your current position. If you can get to a point on the shore before the wolf you will get away. If the wolf beats you there, he's gonna eat you. How do you get away? ((Jay Brady, Feb 15))

[[wiki:donuts:winter2014:wolf|answer]]

===== Black and White Hats =====
In a box, there are 3 black hats and 2 white hats. Tom, Bob and Bill each take a hat from the box and place it on their head without looking. They are lined up with Tom at the back, and Bill at the front (so Tom can see Bob and Bill, Bob can see Bill, but Bill can't see anyone). They cannot see their own hat. They are each asked if they know what color hat they are wearing. Tom says he doesn't know, Bob also says he doesn't know, but Bill says that he does know what color his hat is. How does he know, and what color is his hat? ((Dr. Warnick, Feb. 5))

[[wiki:donuts:winter2014:hats|answer]]

===== Trains and a Fly =====
Two trains are traveling toward each other. Both are traveling at 50 km/h. When they are exactly 200 km apart, a fly starts traveling from one train to the front of the other. Once he gets there, he turns around and travels back to the first train. He continues until the trains meet. How far is the fly's total travel distance? ((Josh Sypherd, Feb. 12))

[[wiki:donuts:winter2014:trainsfly|answer]]

===== Sequence =====
What is the missing number in this sequence? ((Richard Black, Feb 19))
  4 6 12 18 30 42 60 x 102

[[wiki:donuts:winter2014:sequence|answer]]

===== Eggs =====

You have two eggs and a 100 story building. You are to discover the breaking limit of the eggs by throwing them out the window on any floor. What is the minimum number of throws to discover the breaking limit? ((Junming Diao, Feb 26))

[[wiki:donuts:winter2014:eggs|answer]]

===== Equation =====

  1 2 3 4 5 6 7 8 9 = 100

Make the above equation valid only using  the operators + - * / and ().  You cannot rearrange the order of the numbers.

Bonus: Do it with only 3 operators. ((Dr. Warnick, Mar 5))


[[wiki:donuts:winter2014:equation|answer]]

===== An Open and Shut Case =====

You are standing in a hallway with 100 lockers. You walk down the hall 100 times. The first time, you open every locker. The 2nd time, you close every other locker, starting with locker number 2. The 3rd time you go to every third locker. If the locker is closed, you open it; if it is closed, you open it. You continue on this way opening or closing every nth locker for your nth trip down the hall.

After 100 trips down the hall, how many lockers will be left open? ((Josh Sypherd, Mar 12))

[[wiki:donuts:winter2014:openandshut|answer]]

===== The Red Vase =====

By cutting and rearranging the red vase in the image, you can create a square. What is the fewest number of cuts required to do this? ((Jay Brady, Mar. 19))

{{:donutquestions:donutsvase.jpg?400|}}


[[wiki:donuts:winter2014:redvase|answer]]

===== 100 Ping Pong Balls=====

To play this game, two players start with a pile of 100 ping pong balls. On each players turn, they must take between 1 and 5 balls. The winner is the player that takes the final ball. If player A goes first, what should be his first move to ensure that he will take the final ball? ((Junming Diao, Mar 26))

[[wiki:donuts:winter2014:pingpong:answer]]

===== Trees =====

Jack is a farmhand that works for Bill. One day, Bill tells Jack he needs him to plant some trees. They must be planed in 5 straight rows, and each row must have 4 trees. Jack drives out to the field ready to work the next morning. He is surprised when he sees only 10 trees ready to be planted. How does he accomplish his task? ((Jay Brady, Apr 2))

[[wiki:donuts:winter2014:trees|answer]]

===== Eight Eights =====
  8 8 8 8 8 8 8 8 = 1000
Using only the '+' operator, how can you make this a valid equation? ((Dr. Warnick, Apr. 16))

[[wiki:donuts:winter2014:eighteights|answer]]

===== Questions Asked =====
|Richard Black | 1 |
|Junming Diao  | 2 |
| Josh Sypherd | 3 |
|Jay Brady     | 3 |
|Dr. Warnick   | 3 |
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