MATH数学作业代写 Final assessment Assignment description

Final assessment

MATH数学作业代写 In an old Maltese currency, a scudo is equal to 240 grani. There are coins equivalent to 1, 18, 24, 48, 120 and 240 grani.

Please write the statement in Q0, using whichever method of writing you use. There are 6 problems, all of equal weight. Solutions require justification. After you have completed the assignment, please save, scan, or take photos of your work and upload your files to the questions below. Crowdmark accepts PDF, JPG, and PNG file formats.

Q0 (0 points)
I pledge to honour myself and my community by assuring that the work I do on this assessment fully represents my own knowledge and ideas. I will feel proud of my work here when I am done
because I know that it was my own and only mine

MATH数学作业代写

Q1 (10 points)  MATH数学作业代写

n people are operating a space station. Something suspicious is going on there, and they call a vote to voice their suspicions. Each person can suspect any number (including zero) of people
(including themselves) and put them to vote. How many different votes are possible such that there is no group of n people,k>0 , in which everybody is suspecting everybody else? Your
answer may be expressed as a sum.

Q2 (10 points)

A jumping spider lives on a graph  G with x(G)=k , that is properly colored into k colors. The spider can jump from a vertex to any other vertex of the same color, and also go from any vertex to any vertex connected to it by an edge. Show that the spider can reach any vertex from any other in 3 steps or less.

\textbf{Hint:} Show that, in a proper coloring with X(G)  colors, for any pair of colors there is an  edge connecting vertices of these two colors.

Q3 (10 points)
The sequence  fn,n>0.  satisfies the difference equation MATH数学作业代写How many indices  with  fi=0 can there be?

Q4 (10 points)

Find the closed formula for the number of{a,b,c} -strings of length n with no ab  and no bb  substrings (that is, neither of them appear in the string).

Q5 (10 points)  MATH数学作业代写

In an old Maltese currency, a scudo is equal to 240 grani. There are coins equivalent to 1, 18, 24, 48, 120 and 240 grani. How many collections of one or more coins can combine to 1 scudo?
Include any code (Sage or other) you use to compute the answer.

Q6 (10 points)
A labeled graph with   n  vertices has degree sequence MATH数学作业代写 where the order matters. Show that if n >4, there are at least 2 distinct graphs with the same labeled
degree sequence.

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