Due Date: Friday, Dec. 8, 2017, 23:59

1. Each Easter the President and his wife hosts an East Egg hunt for children at the White House. The staff has hard boiled 96 eggs and hidden them on the lawn of the white house. To be as fair as possible and to allow for the chance that each child can find the same number of eggs as each of the other children, the first family wants to be careful about how many children they invite. What are the all of the possible numbers of children that can be invited? Justify/explain your answer.
   
   
2. You have two jugs, capable of holding 31 and 21 gallons of water, respectively.  Unfortunately, neither jug is marked in any way that would allow you to measure how much water was in it if it was partially filled. It is also not possible for the jugs to be marked or altered in any way. You are also near a stream of clear, cold water, so at least you have an effectively infinite supply of water.
   
   Is it possible for you to use your two jugs in such a way that on of them will contain exactly 1 gallon of water and the other jug is empty?  If yes, how?  If no, why not?
   Perform a linear Diophantine tabular analysis as demonstrated in the course notes to justify your answer.
   
   
3. A local florist ordered a number boxes each containing a dozen roses in order to be ready for Valentines day. When the boxes arrived from the supplier the florist discovered that the boxes had been incorrectly packed with eleven roses each. With no time to return the shipment, the florist repackaged the roses into boxes of a dozen each with 3 extra roses left over. Determine the minimum possible number of roses delivered to the florist.
   
   
4. A 32-page newspaper (think of a larger Collegiate Times) consists of 8 full sheets of double truck newsprint. One of these sheets is selected at random, and the four page numbers that appear on it are added together. Can you determine the resulting sum? If so, what is it, and why?
   
   
5. A toy store sells small stuffed bears for $7.00 each and remote controlled cars for $18.00. An electrical power outage at their store results in them making sales by hand. During the power outage they take in $208.00 for the sales of the bears and cars, but they neglected to mark down how many of each they sold. How many of each could they have sold.