St. Paul's Boys admission - our experience

[solimum]

[

"There a number n. n ends in a 9. When the 9 is moved to the front of the number, the new number is exactly 9 times of n. What is the value of n?"

I battled away at this for a while before running out of time and paper! The answer is 44 digits long..... (Parasitic numbers, for anyone still awake)

[expat]

"There a number n. n ends in a 9. When the 9 is moved to the front of the number, the new number is exactly 9 times of n. What is the value of n?"

I battled away at this for a while before running out of time and paper! The answer is 44 digits long..... (Parasitic numbers, for anyone still awake)

Yes, setting up the solution is fairly straightforward but I can't see a quick way to construct the full answer. Though I suppose you only have to do 43 three-digit divisions by 89 to get there.

Btw, the digits repeat, so there is actually a solution every 44 digits.

[iMum]

after googling..

Let the number of the digits be n + 1. Let the last digit be b, therefore,
9(10a+b)=10nb+a
Hence, (10n−9)b=89a

Hence, 10n = 9 mod 89

Dividing 9 by 89, we get,

9/89=0.10112359550561797752808988764044943820224719

Therefore, the smallest possible number is,
10112359550561797752808988764044943820224719

[Amber]

What I would like to know is:

1. Is it realistic to expect a 10 year old to be able to do that?

2. Would a 10 year old selected in that way necessarily perform any better in the long term than one who looked at it with open jaw and said, 'you what?'?

3. Does the school adopt any pretence of that sort of question offering equal opportunity to candidates from all backgrounds to get it right, or even know what it is about?

[expat]

Let the number of the digits be n + 1. Let the last digit be b, therefore,
9(10a+b)=10nb+a
Hence, (10n−9)b=89a

Hence, 10n = 9 mod 89

I'm afraid someone has transcribed the solution badly; it looks like a superscript got lost in the formatting. Where you've written "10n", you actually need "10^n".

[expat]

1. Is it realistic to expect a 10 year old to be able to do that?

All 10 year olds? I wouldn't think so. A very few? Perhaps. Presumably that's why it was a bonus question. At a guess, any progress on this question was used to distinguish between math/academic scholarship candidates.

2. Would a 10 year old selected in that way necessarily perform any better in the long term than one who looked at it with open jaw and said, 'you what?'?

Necessarily? No. But there's a pretty good chance they'll be more interested in math and will stick with it for longer.

3. Does the school adopt any pretence of that sort of question offering equal opportunity to candidates from all backgrounds to get it right, or even know what it is about?

I believe this question is more equal opportunity than the triangular numbers one. Afaik, triangular numbers are not covered in the KS2 curriculum but they are in the KS3 curriculum, early enough so that some primaries cover the topic. While that's also somewhat true of the algebra needed to set up the solution to this problem, I'd be stunned if any primary covered the number theory needed to make the final step to grind out the full answer.

[LolaD]

What I would like to know is:

1. Is it realistic to expect a 10 year old to be able to do that?

2. Would a 10 year old selected in that way necessarily perform any better in the long term than one who looked at it with open jaw and said, 'you what?'?

3. Does the school adopt any pretence of that sort of question offering equal opportunity to candidates from all backgrounds to get it right, or even know what it is about?

Very good questions!

I am stunned by such high expectations of 10 year olds, scholarship material or not. Don't even get me started on the ridiculous amount of time given to decipher an insane question!

[expat]

I am stunned by such high expectations of 10 year olds, scholarship material or not.

How would you propose to distinguish between scholarship candidates, if not by giving them questions which only a very few would be able to answer?

[Surferfish]

I can only assume that they don't expect every successful applicant to be able to answer this type of question.

Perhaps these questions are used to try and identify super intelligent genius type children who might otherwise slip through the net by performing less well overall (maths whizzes who don't know their Charlotte from their Emily Bronte... )?

If a future Nobel prize or Fields Medal winner had been educated at St Paul's then that's going to be great PR for the school.

[Amber]

I am stunned by such high expectations of 10 year olds, scholarship material or not.

How would you propose to distinguish between scholarship candidates, if not by giving them questions which only a very few would be able to answer?

I think I would be looking for creativity, divergent thinking, a 'spark' of some kind, which maybe could even be demonstrated in a rather less rigid and stereotypical 'bright kid' kind of way, to be honest, and may even give some who hadn't spent their childhood being tutored an outside chance of success.