Recently I have been applying to a couple of jobs for next year, and have beenquite fascinated by the anxiety other people express over the whole applicationprocess. It seems everyone is so intent on being perfect for the job they’reapplying for, that they don’t seem to notice that if they have to ‘change’ whothey are to get the job, the job probably won’t suit them. So they doctor uptheir C.V’s and buy different clothes and attend the interviews readyingthemselves to answer in such a way that their weaknesses become strengths….

The best one I’ve heard from this is: “what is your biggest weakness?”

“I’m dedicated to my work, so I often work straight through a lunch break”.

Yeah right.

My favourite part of interviews are the questions that makeyou think. Asking what I would do in a given situation is boring, but asking mehow to solve an abstract idea – that’s fun.

My girlfriend had an interview a few months ago, and one ofthe questions was:

using square tiles that have an area of 1 unit squared, how can you lay thetiles such that the number of tiles used is twice the number of tiles in theperimeter?

the way people approach this is fascinating. Most of us will start writing outequations, so perimeter of a rectangle is 2 x (width+length) and the area iswidth x length, so, using w,l to denote width, length respectively,

4(w+l)=wl

⇒4+4l/w=l

which isn’t easily solved. It would probably be best to start throwing integersinto the equation, and see what comes out.

So if we define w as 8, we get 4+l/2=l⇒4=l/2 ⇒ 8=l so a square of 8 by 8 works! Right?

Wrong.

We forgot to notice that thecorner tiles are counted twice. The perimeter calculation should actually be2*(w+l-1) (but the area still stays the same).

so

4(w+l-1)=wl

⇒ 4+4(l-1)/w =l

again, try values of w

W=8

4+(l-1)/2=l

8+l-1=2l

7=l

Which gives a perimeter of 28tiles and an area of 56, which works.

But to do this in an interviewwhere people are stressed out….that’s a bit more tricky. You’ll forget todouble the perimeter. You’ll forget the repeated tiles. And you won’t noticethat if you tile around the equator, you simply need to place 4 rows of tiles,one above the other, to satisfy the requirements…

There are quite a few questionslike this.

An alternative solution is tocreate a gold cutting device that has 6 knives. Then you just need one cut.

Now, from my limited experience ofinterviews and applications, it seems that most companies claiming to belooking for mathematicians are actually looking for a computer or a softwaredeveloper (which is good news to software developers!). Almost all graduatejobs base part of the application on marks attained at university. Interestingly, those marks are made up ofexams, tests and assignments. Assignments seldom give more than 20% towards the final mark. Roughly 40% of theassignments are based on an ability to think like a mathematician. The rest is rote learning/memorisation or useof a method. Unfortunately, the examsand tests are also based on this. This meansthat most courses have at most 10% of the course based on the ability to think,and 90% on being able to memorise proofs and theorems and methods.

This is all well and good…except for a little thing called the internet. Throughthe use of google, wolframalpha and Wikipedia, that 90% of the course can bedone by someone with no previous knowledge of the course. I would also guess that they can do it moreaccurately, and faster.

So to base your applicants ontheir university scores seems to me to be a waste of time. If that is all youwanted, you’d be better off getting a software developer or simply using thosethree sites – this way will be much cheaper! If you ever come across a problemyou can’t solve using those sites…well, then there isn’t a high chance yourgraduate with straight A’s could have solved it either…

But enough of that. It’s fairly obvious I have crap marks and think I’m abetter mathematician than those marks show, but that’s my opinion. I likesolving problems, and this is a taster of the next post:

what do the numbers 1089 and 495 have in common?