1. CMPF144 FUNDAMENTALS OF COMPUTING THEORY Module 10: Applied Mathematical - Logical Knowledge Riddle/Puzzle

2. Module 10 CMPF144 Fundamentals of Computing Theory Slide 2 Review Many problems have been approached during this course; some introduction has been provided on HowTo tackle a problem. One task or another turned out to be 'solvable'; others could not be solved. The advances of Computer Science are closel y related to the development of mathematics and based on logics.

3. Module 10 CMPF144 Fundamentals of Computing Theory Slide 3 History Computer Science itself is a result of searching to solve mathematical problems; mainly those that require a huge amount of calculations, too many to be done by humans. Another aspect of the history of Computer Science were the efforts to create a 'human-like' machine. Any such machine needs to have human-like features as responding to a given question; even pretending to be a human.

4. Module 10 CMPF144 Fundamentals of Computing Theory Slide 4 Computer Science ? The Dictionary Server of the MIT ( Massachusetts Institute of Technology) defines: “Computer Science n : the branch of engineering science that studies (with the aid of computers) computable processes and structures syn: computing” Computable Processes, these are processes that can be calculated or approached with logic.

5. Module 10 CMPF144 Fundamentals of Computing Theory Slide 5 Riddle ? Many people like (or even love) to solve puzzles, jigsaws, quizzes, riddles. The MIT Dictionary Server gives us: “Riddle Rid"dle, n. [...] Something proposed to be solved by guessing or conjecture; a puzzling question; an ambiguous proposition; an enigma; hence, anything ambiguous or puzzling.”

6. Module 10 CMPF144 Fundamentals of Computing Theory Slide 6 Puzzle - Riddle ! We met some problems of 'Playing With Matches' that could be reduced to a rather simple solution. Knowing this solution, we could extend this solution to other, larger, tasks by throwing out all problematic elements easily until we reached the minimal set; with the known solution to it. This is not always the case; often it is impossible to eliminate (throw out) additional elements.

7. Module 10 CMPF144 Fundamentals of Computing Theory Slide 7 First Riddle A typical, well-known riddle is the one taken from Lewis Carroll's Alice in Wonderland: Knights or Knaves ? Imagine there are two types of people, Knights (who always tell the truth) and Knaves (who always lie). There are three such people sitting under a tree, A, B and C. A says, "All of us are Knaves." B says, "Exactly one of us is a Knight." What are A, B and C ? It is possible to tell!

8. Module 10 CMPF144 Fundamentals of Computing Theory Slide 8 Knights or Knaves ? http://www.cheltcoll.gloucs.sch.uk/depts/maths/mathsp6.htm

9. Module 10 CMPF144 Fundamentals of Computing Theory Slide 9 More Riddles ! When you have solved the riddle of Knights and Knaves, You may continue to look at the extensive collection of riddles at http://www.ocf.berkeley.edu/~wwu/contents.shtml They are sorted into easy med(ium) hard

10. Module 10 CMPF144 Fundamentals of Computing Theory Slide 10... And More Types... Plus, there are special sections for Computer Science (cs) and those collected who went to job interviews at Microsoft (m$). Microsoft is well-known for asking riddles from those who apply for a job. Here the students can find a good collection of those. Very often there is no (single) solution to these riddles; non at all, an estimation or assumption required, simply a decision to be taken.

11. Module 10 CMPF144 Fundamentals of Computing Theory Slide 11 Specific Advantages... these are the most valuables, somehow, because they require the student to ponder, if there *is* a solution to these riddles at all; find encouragement to take a reasonable guess find encouragement to take a reasonable decision invent a - nevertheless - useful answer

12. Module 10 CMPF144 Fundamentals of Computing Theory Slide 12 Task 1 Search and identify a riddle (one) out of those offered on the site (suggested: ‘medium') and discuss it in small groups. Like earlier in our course, the solution itself is very uninteresting ! Therefore, 'sneaking' is highly discouraged. The intention is to identify one of those riddles and work on that like on the 'Knights or Knaves ?' above. Feel encouraged to add an own post; on own opinion, ask a question, etc. in the Forum

13. Module 10 CMPF144 Fundamentals of Computing Theory Slide 13 Task 1 - Deliverables Be able to present the riddle to the other students. 'Presenting' here entails to explain and detail the problem, plus the steps, ideas, plays, programs, etc. thought out within the group to approach the problem. Grading will not be based on having found 'a solution', but rather on the ability to explain the problem, answer related questions, detail the approach of the problem. Be prepared to reason your answers.

14. Module 10 CMPF144 Fundamentals of Computing Theory Slide 14 Task 2 Identify a riddle out of those from the Microsoft section; once again in groups, and work on it just as well. Preferably, a riddle without (obvious) solution should be selected. If this is unclear, the meanwhile famous bus, available under the m$ section http://www.ocf.berkeley.edu/~wwu/cgi- bin/yabb/YaBB.cgi?board=riddles_microsoft;action=display;num=1028571067 can be considered a good example.

15. Module 10 CMPF144 Fundamentals of Computing Theory Slide 15... Reasoning Microsoft seems to like this one in interviews and going through the 'answers' given, the students may guess that what is required is an analysis of the problem (it seems there are too few indications to come up with the answer) possible questions to get further eventually daring a logically correct assumption finally a decision, an answer, a suggestion - in no case, however, 'silence'

16. Module 10 CMPF144 Fundamentals of Computing Theory Slide 16 Deliverables - Task 2 Whichever riddle is used, the students work it out similar to the first one. They are ready to present it freely, draw it, discuss it in front of the others report on their additional question(s) explain their decisions (either individually or in groups), their answer(s), and why.

17. Module 10 CMPF144 Fundamentals of Computing Theory Slide 17 The End ! Have Fun ! - Have Even More Courage Than Fun !!