My name's Gavin Lowe, I'm a tutor and director
of studies for Computer Science at St Catherine's

college Oxford. This video is going to be
a demonstration admissions interview, we're

going to try and show you how we run our undergraduate
admissions interviews for Computer Science

and in particular how we run them using online
technology. So with me I've got Alastair Janse

van Rensburg who's another tutor at St Catz
and Tom Aston who's an undergraduate at St

Catz. Tom's just about to enter his second
year. So in a moment we'll be into giving

a demo interview to Tom, see how he gets on.
First of all let me just say a little bit

about how we run interviews. I normally start
interviews by a little bit of general discussion

... try and get to know the candidates a little
bit better, find out what motivates them,

sometimes at that point I'll ask a question
about something on their personal statement,

sometimes I won't, I won't do that today.
However most of the interview is made up of

technical questions, some mathematical problems
or puzzles, to try and assess the candidates

technical ability that how will they help
cope with the Computer Science degree at Oxford.

So for online interviews we use an app called
Miro we'll use it, we'll see it in a bit,

it's an online whiteboard app, ... my experience
is that most candidates get on fairly well

with that ... but it's the sort of thing that
if somebody messes up we're not too worried

about that, we're more interested in how good
candidates are technically. So we want to

see ... how well they cope with the problems
that we give them ... whether they think logically

and come up with good ideas for tackling the
problems. Also are they able to explain their

thinking reasonably, of course we don't expect
a perfect explanation in real time, but I

hope we can have a conversation where we get
to understand what the candidate is thinking.

And also the other way around, can the candidate
pick up hints from us, ... well really we

want to assess whether candidates will cope
well with the interactive style of teaching

that we have at Oxford, so we want to see
that they actually will learn from what we're

saying. At the end of the interview ... we
normally give the candidates a chance to ask

their own questions if they have any, but
we won't be doing that today. Okay so we're

going to do a 20-minute sample interview,
that's a bit short really normally we actually

allow 30 minutes ... for an interview but
it's gonna be a little bit shorter today.

Okay so let's see how Tom gets on.

Hello Tom, so thanks very much for coming
for interview, ... perhaps we can start can

you just tell us why do you want to study
computer science? I study computer science

because I find it incredibly interesting how
an inanimate device like a computer which

fundamentally like built out of silicon, can
sort of work from the very smallest elements

like transistors all the way up to like for
example Teams that were doing this interview

over, ... and how that can also be abstracted
out from like small logic gates up to adders

up to like applications and operating systems.
Okay can you tell us about something interesting

you've done in the area of computer science
maybe an interesting program that you've written?

Although it's quite simple probably my favourite
program that I've ever written was just a

small mini max algorithm for ... noughts and
crosses. It's like yes it's quite simple and

the implementation wasn't too hard but I found
really neat how like an algorithm like that

can be implemented and how like you can basically
create an unpeaceable AI for a game as simple

as noughts and crosses. Okay that sounds interesting,
thanks. Okay so let's move on to some technical

problems ... so for the purpose of the recording
I'm going to share my screen looking at Miro

Okay so there's a question here ... so let
me read the first bit through to you Tom and

then you can have a go at it. So Alice plays
a game with her friends Sam and Pam. In each

of the scenarios below she chooses two positive
integers x and y, so one less than or equal

to x, x less than or equal to y, and she whispers
the sum s which is x plus y to Sam and whispers

the product p which is x times y to Pam. Sam
and Pam have to try to work out what x and

y are. They're all expert logicians and they
always tell the truth. Okay so part one Alice

chooses two positive integers x and y as I
just described, and whispers the sum to Sam

and the product to Pam. Sam says I know what
x and y are, what can you say about x and

y? Okay so for Sam to know what x and y are,
then x plus y must ... well s must specify

two distinct integers. I think the most obvious
or the most obvious initial case is if s is

two because then that that just gives x is
one and y is one. Would there be any cases

beyond that .. I think if s is three then
that also precisely specifies x and y so we

have x is one and y is two. Yeah that's right.
So two equals one plus one three equals one

plus two but then beyond I think those are
the only cases because four could be either

one and three or two and two so it doesn't
give us the exact. Yeah we'll be able to work

out in that case and for larger values of
s? That would hold me on because ... any large

number of s can be one plus ... actually s
minus one or. Or similarly with two. Yeah

or similarly with two yeah exactly. Okay good
let's have a look at part two then ... so

Alice now uses new values for x and y and
whispers the sum to Sam and the product to

Pam. Pam says I know what x and y are what
can you say about x and y?

So in this case we have x and y as precisely
precisely specifying p, which means that p

must only have two factors because otherwise
we don't know what x and y are, which tells

us that p must be prime ... and if p is prime,
because we have x as less than ... well x

has to be ... well less than or equal to y,
but since it's prime we know x is less than

y, so we know that x well x must be one, and
y must be the value of s that Sam is told.

You mean the value of p that Pam's told? Yeah
the value of p that Pam's told, sorry, which

means that the value that Sam is told is p
plus one

Right so. So does Sam now know what x and
y are?

Yes so Sam knows that x equals one, and y
is s minus one. Yeah that's right, you actually

missed a little bit with Pam ... normally
the number one is not considered to be a prime

number. Yeah sorry. So okay so if actually
p is one then x is one and y is one fairly

obviously, okay good. Part three Alice again
chooses new values for x and y and whispers

the sum to Sam and the product to Pam. Pam
says I don't know what x and y are, Sam then

says I know what x and y are but I didn't
know before Pam said that. Okay so first of

all can the sum be less than four?

No the sum can't be less than four because
in part one, ... like the minimum sums got

to be two, and in part one we solve for both
s equals two and s equals three that tells

Sam precisely the values of x and y i.e. that
he knows he knows values of x and y before

Pam says that they don't know what x and y
are. Yeah that's right if the sum is less

than four then Sam would know immediately.
Okay part b, suppose the sum is four, what

are x and y? So if this sum is four then that
either gives x equals one y equals three or

x equals two y equals two ...

so Pam doesn't know what x and y are ... if
however, well, in the case that x equals one

y equals three then Pam knows that p equals
three, and in the other case ... Pam has p

equals four. If p is three then Pam has been
given the prime number which means that ... she

knows the values of x and y, however since
she doesn't know what the values of x and

y are, we must therefore have that x equals
two and y equals two. Right so by the fact

that Pam doesn't know what x and y are we
can eliminate x equals one y equals three

and in the case of ... so how does Sam now
know what x and y are? Well Sam knows that

sum is four so in effect before Pam says anything
Sam knows that so either ... x equals one

and y equals three or x equals two y equals
two and in this case, when Pam says that I

don't know what x and y are, that gives us
the additional knowledge that therefore p

cannot be three. Right. Because in that case
... she'll know therefore we know that must

be p equals four so x equals two y equals
two. Yeah good. Okay ... part c, can the sum

be five?

So if we consider s equals five then that
would give

x one y equals four or x equals two y equals
three as the only cases to consider themselves

must be, well, less than or equal to y ...

so

is that yeah ...

So you consider those two possibilities ... are
they consistent with the story? So with, so

in both cases, well, first one has gives p
equals four the second gives p equals six

... if p equals four then Pam doesn't know
why x and y are, again because we also have

x equals two y equals two ... and then if
p equals six then Pam also doesn't know y

x and y are because we could alternatively
have x equals one y equals six. Right. So

Sam doesn't gain any information from that.
Yeah that's right so ... in both cases Pam

would say I don't know what x and y are so
Sam doesn't learn anything from that. Okay

part d then, can the sum be more than five?
Okay ...

so if this sum was more than five, then we
would have at least three ... pairs of x and

y to consider. Right. So... s equals let's
say six as an example but it will hold then

we have x equals one x equals two x equals
three all to consider ...

so when Pam

yeah that would work for x, s equals six so

no I'm sorry ... y equals five, y equals four,
y equals three, which gives p equals five,

p equals eight and p equals nine

so in this case

... actually yeah in this case the additional
knowledge that ...

Pam doesn't know where x and y are doesn't
actually help

because if if Pam knows what x and y are we
have that x equals one and y equals five because

five is prime, however the other two possible
values aren't prime, so that doesn't actually

tell us anything additionally. So at least
those latter the case of x equals two x equals

three Pam wouldn't know what x and y are,
so

so

Pam only knows what x and y are when without
any additional information when x is one ... however

since x is less than y x is one only occurs
once so the additional knowledge that Pam

Pam doesn't know where x and y are only eliminates
the x equals one case every time, however

for s equals 6 and above we always have at
least two further cases to consider, so it

doesn't actually yeah it doesn't tell us sufficient
information to figure out x and y. Yeah that's

right so in each case it'd be at least two
possibilities where Pam doesn't know what

x and y are and Sam won't be able to tell
the difference between those. Okay so to actually

summarize question three the only solution
we got there was x equals two y equals two

happens to be the only solution to that. I
think what I want to do now is skip part four

because we we're actually quite tight on time
but we can go on to question two and I'll

hand over to Alastair ...

you all need to advance on the pdf so Alastair
if you want to take over. Okay .. Tom can

you see the second page of questions there
starting with consider the following list?

Yes, I can now. Excellent okay I'm going to
read that out for you and then we'll talk

about the questions below. Consider the following
list of five numbers: one, three, two, four,

nine. For some numbers one less than equal
to a, less than equal to b, less than equal

to six, we're going to define the sub list
from a to b to be the consecutive numbers

from the list starting at position a and up
to but not including position b, so for example

if we wanted the sub list from two to five
that would be three to four and the sub list

from four to six is four, nine, and so that's
the six going off the edge there but we're

just ignoring that there, because we want
up to the last one, and then the sub list

from one to two is it's just the element one,
and then finally just as a convention we're

going to say the sub list from from x to x
from for any x there is defined to be just

the empty list there. We're also going to
say that s of a b is going to be the result

of adding up all the elements of the sublist
from a to b. So the first question I want

you to answer here is ... how many sub lists
are there that start from the first element?

Starting from the first element there would
be five sub lists. Okay can you just go through

which what those would be? Sure so you have
a first one is going to be the empty list.

Okay. Then just the first element itself,
first two elements

first three elements so one three two and
finally first four elements one three two

and four

Okay well why do we stop there?

so if you just look at the definition. Yeah
we can go ... up to the last one sorry. Exactly

but so you have spotted that the empty list
is one of those lists so that's good, okay

so now how many sublists are there starting
from any element, not just from the first

one?

so from any elements in this list if we

from any elements in this list it would be

well for the ... first element we have ... six.
Yep. Six sublists. From the second element

we'll have an empty list, list of one, a list
of two, lists of three of length three, and

a list of lengths four, but not the list length
five. Yeah. So in this case it would the total

number of sub lists from any element would
be seven minus n where we let n to be the

position or index. Okay so if you add all
those up you're gonna get some some number

there. Have you double counted any lists there
so do you have any lists in those set of lists

that would be the same?

... when you say in that set of lists what
do you mean by that? So for instance your

list starting from the first element there
you have the empty list and then one and then

one three etc, ... what are your elements
starting, sorry what are your sub lists starting

from the second element? From the second element
the empty list will obviously be the same

... but then otherwise there wouldn't be any
overlap with the elements in the first one,

so we'd have empty list.... So can you spot
the duplicate there where you have two, two

lists that are being counted, or whether one
is being counted twice? Yes so the empty list.

Excellent okay yeah so we can count that and
get rid of that, but okay so moving on to

question two here then, ... can you tell me
what the value of s two six is that's the

sum of the elements of the list two six, sublist
two six

the sub list two six involves ... starts from
index two so that would be so three plus seven,

two plus the fourth element plus the fifth
element which works so three plus two plus

four plus nine is eighteen. Excellent okay
... so now what we wanna do is do a bit of

manipulation with that so I've got an expression
there in part three there, says there's s

of a b is s of one b minus s of one a. Can
you explain to me why that expression is true?

Okay so

okay ... I think I want this

right so if we have

oh okay ... so in fact the value of s of a
can be if we just draw a list currently from

one three

two four nine ... if we let ...

but basically the sub list, well the value
of s from one to b .... well obviously includes

all the values from one to b and yes these
... sublist the value of s records 1 comma

a includes with values from 1 to a, which
means that all the values less than a of so

all the values of index of less than a are
included but in both the summation from one

to b and also the summation of one to a. Yeah.
Then as a result they get

like this the subtraction effects removes
them. Yeah exactly. So yeah the only values

that aren't then eliminated are the values
that occur from index a onwards in the expression.

Yeah up to b. Yeah that's good all right.
That's why they're equal. Yeah excellent okay

so ... part four... I'm sorry I'm going to
just pop in at this point ... I'm afraid we're

basically out of time at this point we've
had our 20 minutes and ... we never get through

all the questions so don't worry about that
but but thank you very much Tom for that ... bye

for now. Bye thanks.

Okay so I think Tom did very well there generally
... I sort of expected that ... Tom's already

been interviewed once and he got a place on
the basis of his interview so he's already

shown that he is very good, has the sort of
skills that we're looking for. In addition

he's now about two years older and has two
years more experience than when we first interviewed

him and hopefully he's learned some things
in that intermediate time. He didn't answer

all the questions in the time available but
we pretty much expect that ... anybody, in

addition we only gave him 20 minutes whereas
normally we'd allow 30 minutes for an interview

like that, so ... anybody who gets about that
far in 20 minutes is almost certainly going

to get a place, so he did very well and we're
not really expecting all candidates do that

well. In particular one thing he did work
very well was just not to get muddled. It's

quite common, particularly the first question
we asked there, for candidates to just get

completely stuck for a bit or to spend time
going around in circles ... a common thing

that people do is actually repeat the earlier
parts forgetting that they've already solved

a particular sub problem and go back and solve
it again ... even though effectively they're

just repeating an earlier part. One thing
with hindsight I should have stopped him doing

is that he rubbed out his answers to each
of the individual parts, actually it would

have been a better tactic for him to have
left those there so that you could refer back

to earlier parts when answering later parts.

Yep so generally he did very well ... understood
all the questions well, thought very clearly,

... there were a couple of bits where he was
just a little bit slower ... he was in the

second question with Alice he was a little
slow to spot that the the empty list was repeated

but we expect the odd oversight like that
and his final explanation might have been

a little bit clearer ... I think it's the
best way to answer that question is to draw

a picture highlighting the different regions
that different parts of the equation represented,

but these sort of minor criticisms and and
overall that was a good performance, that's

the sort of performance that would normally
get somebody a place in Oxford. Okay so I

hope this video has been useful and interesting
to you and helpful to show you how we run

these sorts of interviews.