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1 you bring a bag of 12 snacks to an animal shelter and discover that there are 18 animals there to be fair you dont
1 how many words of length w can be made using an alphabet with l letters2 how many telephone numbers have no 0 in the
now suppose that you want to solve the restricted trench puzzle the setup is the same as the trench puzzle of the
you are in a strange multi floor shopping mall whats strange about it is the placement of the escalators for every
consider the sequence given by a1 1 an an-1 2n- 3 can a technique from this chapter be used to find a closed form
write out several rows of pascals triangle circle the first 1 of any row go over one entry to the right and then one
choose one of the sequences you generated above and input the first five terms into the online encyclopedia of integer
for each of the following recurrence relations write out the first several terms of the sequence at least five and use
1 suppose you have a yam with n-1 cuts carefully slice the yam in two and look at the freshly cut faces what do you see
1 fill in as much of this table as you canit would be a good idea to collaborate with other groups of people to share
try to prove any conjectures available to you notice that because the only information you started with was a pizza and
1 how many chunks of yam can you obtain when using exactly two cuts2 what is the largest number of yam chunks
1 consider a long strand of one-dimensional spaghetti what is the largest number of pieces of spaghetti you can obtain
1 start conjecturing about yams if you havent already do you see a possible recurrence relation how about a closed-form
suppose that you are given the roots to a characteristic equation and they are -12 and -3a what is the characteristic
1 what is the largest number of pieces of pizza you can obtain using exactly three cuts try drawing a few pizzas of
1 draw a tree that has exactly two leaves2 draw a tree that has exactly three leaves3 give an example of a sub graph of
1 show that every connected graph has at least one spanning tree by giving an algorithm for finding one2 did your
1 compute the total weight of each of the spanning trees shown in figure 102 which has the smallest weight is that the
1 if an edge-weighted graph has several edges of the same weight there will be more than one way to order the edges
let us generalize problem 20 suppose we wish to create a geometric structure from k points in the plane and that we
we are going to construct a geometric structure from a set of lines using a finite number of points in the plane
we will triangulate as in problem 18 a convex polygon that has a convex polygonal hole cut out of its interiora draw a
a triangulation of a convex polygon is a partition of that polygon into triangles that does not introduce any new
1 considering the previous two exercises a draw the first four square numbersb draw the first four triangular