The MU Time Travel Society $($MUTTS$)$ has invited seven famous historical figures to each give

a lecture at the annual MUTTS convention, and you've been asked to create a schedule for them.

Unfortunately, there are only four time slots available $(1pm-4pm),$ and you discover that there

are some restrictions on how you can schedule the lectures and keep all the convention attendees

happy. For instance, physics students will be disappointed if you schedule Niels Bohr and Isaac

Newton to speak during the same time slot, because those students were hoping to attend both of

those lectures. After talking to some students who are planning to attend this year's convention,

you determine that they fall into certain groups, each of which wants to be able to see some subset

of the time$-$traveling speakers. $($Fortunately$,$ each student identifies with at most one of the groups.$)$

You write down everything you know:

The list of guest lecturers consists of Alan Turing, Ada Lovelace, Niels Bohr, Marie Curie,

Socrates, Pythagoras, and Isaac Newton.

a$.$ Turing has to get home early to help win World War II$,$ so he can only be assigned to the $1pm$

slot.

b$.$ The Course VIII students want to see the physicists: Bohr, Curie, and Newton.

c$.$ The Course XVIII students want to see the mathematicians: Lovelace, Pythagoras, and Newton.

$7$ people $4$ slots. d$.$ The members of the Ancient Greece Club want to see the ancient Greeks: Socrates and

Pythagoras.

e$.$ The visiting Wellesley students want to see the female speakers: Lovelace and Curie.

f$.$ The CME students want to see the British speakers: Turing, Lovelace, and Newton.

g$.$ Finally, you decide that you will be happy if and only if you get to see both Curie and Pythagoras.

$($Yes$,$ even if you belong to one or more of the groups above.$)$

i$)$ Write down the set of variables, the set of domains, and the set of all constraints.

ii$)$ Draw the constraint graph for this CSP$.$

iii$)$ Search for a solution using backtracking search with forward checking and domain$-$

independent heuristics. Mention each step in the solution$-$finding process clearly.

$[1+2+3=6$ Marks $]$