Final Lecture

Instructions in Exam

• ANSWER 2 QUESTIONS.• There will be a choice of 3 questions.• Each question will be in parts e.g. a, b, c.• You can see the marks awarded for correct

answers for each part.

Tips• Before Exam, try past exam papers under exam conditions • (e.g. turn off your phone and see if you can answer an exam paper

comfortably within the time).• Read all of the questions. • Sketch out your answers. • Keep track of time e.g. spend about half the time on each question. • You do not need to cheat (e.g. take in formula). • Any reasoning you do with diagrams, I would do in pencil first, • mistakes can be rubber out (and you can write in pen later). • This is an easy exam so relax and do not worry. • WRITE NEATLY

Time and Place

• 04:30PM-06:30PM, 14/01/2008• Algorithmic Problem Solving• Year 2 CS; Year 2 CSM• SSB302

a≡b verse a=b• With just 2 variable these are the same. • With 3 or more variables they are different. • a=b=c (read conjunctively) mean they are all the

same value• just like integers or reals in maths. • a≡b ≡c (read associately) i.e. a≡(b ≡c ) or as (a≡b)

≡c• but actually these are both the same so we can

forget about the ()• but a=b=c is not the same as a≡b ≡c

Knight and Knaves - again :(• Knight tell truth, Knaves lie. • (let 1 be Knights 0 be Knaves)• If we ask A a Yes/No Question Q, the response to the

question will be true in 2 cases• 1. the question is true and A is a Knight• 2. the question is false and A is a Knave• (in the other 2 cases it is false)• We can summarize this as Q=A • where Q is a yes/no question (i.e. a Boolean

proposition)• and A is the Boolean proposition "A is a knight"

• Question to ask• We want to find if A and B are the same type

(for example). • The required response is A=B (i.e. A and B are

the same type)• From the previous slide we know Q=A, • therefore (Q=A)=(A =B), • what does this simplify to?

Mex Numbers (again)

• draw a graph (random) and label with letters. • How is a state described. • Now label mex numbers• A mex number is the smallest natural number

not in the mex number of the successors.

Mex Numbers in Sum Games

• In a matchstick game we can remove 1 or 2 matches, label the diagram with a pattern.

• What it the mex number of the nth position?• How do we play the sum game?• How do we play a pair of matchstick games?• How about a random graph and a the

component game from coursework 2.

Fuse Clocks – show fuseclock.ps file

• Given two fuses which burn for m and n, create as many clocks as possible

• Clearly m and n need to be different.

Before the exam.

• Seminars. • If you have problem, mail me at • John.woodward@nottingham.edu.cn• John.r.woodward@gmail.com• Good luck in Exam.