MAT Prep Thread 2018

This is a guess. But they imply that
if a-d = c-b, then
ad ≠ bc.
Therefore c > a, b > d or c < a, b < d. This contradicts (i). Therefore (d) is the answer. As I say, complete guess and probably wrong! I’ve just started looking at MAT papers a few days ago.

If a=c and b=d,
ab=da=cd=bc (always whether a,b,c,d are complex,irrational whatsoever)

2002 Q5 (Hexaglide)

(i) 6 moves: Call the columns A, B, C. There are 6 possible positions where we can make the 2 "A" moves, so 6C2 ways of choosing when to make the A moves. This leaves 4 positions for B, so 4C2 ways of choosing when to make the B moves. The C moves are then forced. So 6C2 x 4C2 = 6 x 5 x 4 x 3 / 4 = 90.
7 moves: No way of doing it in 7 moves - if you count the "vertical distance from base position" (summing for each column), we see this distance is always equal to the number of moves modulo 2. Since the final position has vertical distance 6, the number of moves must be even.
8 moves: Obviously one column makes 4 moves, 3 forwards, 1 back. Suppose it's column A. There are 8C4 choices for where the 'A' moves go, and then 4C2 choices for the 'B' moves. 'C' moves are again forced. This gives 8x7x6x5/24 x 6 = 2 x 7 x 6 x 5 = 420 possibilities. We then need to consider the possible order of A-moves. We can't start or end with a backwards move, so the possibilities are Forwards, Backwards, Forwards, Forwards or Forwards, Forwards, Backwards, Forwards. So that gives 840 possibilities. Finally multiply by 3 for possibility of making the 4 moves in columns B or C for a final answer of 2520.

(ii) (a) Yes. White moves A,B forwards while Black shuffles C forward and back, then White moves C forwards.
(b) No. Define D to be the sum of the vertical distances between the white and black pieces (so initially D = 3). Again it is easily seen that D has opposite parity to the number of moves made (i.e. D is odd when an even number of moves have been made and vice versa). So D is always odd when black has just played, and therefore cannot be zero.
(c) Obviously yes, since black can never win.
(d) No. Again, on white's turn, it must always be the case that D is > 0. So white is never "blocked" and can always advance. It follows that white can always win after 3 moves.

(iii) (a) No. Note that in the final position, it must be that white just moved. So an odd number of moves have been made. But (defining D as before), D is initially 8 and so has equal parity to the number of moves made. So D is odd when it is black to move, and so D is never zero when it is Black's turn to move.
(b),(c), (d) are effectively answered together. On black's turn, since D > 0, black can always advance. It follows that black has a forced win after 12 moves. (Edit: 8 moves. I can't count...)
So (b) Yes, (c) No, (d) Yes. (Edit: meh, neither can I read the question. Of course, in an exam I'd actually be able to look at the question and my answer at the same time

What should be the answer? Boris?

That's not what I got...I think that's the answer they want you to get without thinking, but then if you work it out, it should be Doris...
A=$\frac{1}{3}$ as P(5 or 6)=$\frac{1}{3}$

B=$\frac{2}{3}\times \frac{1}{3}=\frac{2}{9}$

C=$\frac{2}{3}\times \frac{2}{3}\times \frac{1}{3}=\frac{4}{27}$

D=$\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}=\frac{8}{27}$

A>D>B>C
Therefore D is second most likely to do the washing up.

Let me know if you need any further explanation as being so late I'm not sure if I've explained it properly...

Thanks . Got it.

Is probability even in the syllabus?
Which years question is this if you don't mind me asking?

I do not know whether this thread is the right place to ask this question, but does somebody have any idea with regards to the number of places available in University College Oxford for reading Computer Science/Computer Science and Maths/Maths and Statistics? I would be grateful if someone could provide me with more information on this subject.

just check out their website. They have details of number of students that they take and the acceptance rate. for example https://www.ox.ac.uk/admissions/undergraduate/courses-listing/computer-science?wssl=1

Unfortunately , their website does not have details for the number of places in any subject . I was wondering if someone could tell me.

Unfortunately , their website does not have details for the number of places in any subject . I was wondering if someone could tell me.

what do you mean?
I can see it in the right-hand corner.
On the computer science Webpage, it says that the intake is 31 students. For Maths, it says the intake is 183.
Maybe I misunderstood your question. If that is the case sorry for wasting your time hahaha.

These tables should help

https://public.tableau.com/views/UniversityofOxford-CollegeSuccessRates2017/CollegeSuccessRateswithCommentary?:embed=y&:display_count=yes&:showTabs=y&:showVizHome=no

Rohan , even I know that. I wanted to know the places specifically at 'University College' Oxford. It is the name of an Oxford college.

Aah sorry bro. I forgot to read College so was just thinking University of Oxford. My bad.
I will try to find something, and if I do I will let you know.
Sorry again for wasting time.

Don't worry. Its okay.
By the way, is it worth trying old Cambridge CSAT papers (the website says that the CSAT is similar to the MAT. ) I tried a few questions and the style of questions were quite different.

Rohan, to which Oxford college did you apply? St. Catz?

Professor, I would like to know the seats specifically available at University College for Computer Science. I contacted them around 5 days ago, but they have not responded.(FYI, I contacted them via the 'Contact Us' form on their website.

I work for neither University College, nor the Computer Science department.

On the tables I linked you to, you'll see that the number of offers made in CS by University College were 3, 0, 2 in the last three years.