Listen With Others

Are you sitting comfortably? Then we'll begin

Listener 4270, Alma Mater: A Setter’s Blog by Oyler

Posted by Listen With Others on 24 December 2013

Alma Mater. The auld grey toun of St Andrews or Kilrymont as it was once known from the setter’s perspective.

The only benefit of teaching in the only split site secondary school in Scotland – Madras College St Andrews – is that when you are non-contact and haven’t received the dreaded yellow slip (why are all ‘please take’ slips on yellow paper?) then you are essentially free to do as you please. This normally means travelling between the two buildings – the junior S1-3 building in the SE part of the town and the senior S4-6 building which is in the centre of town. However staff can be seen wandering around the town having nipped out to the bank or post office but more usually a coffee shop or supermarket. The University of St Andrews has a shop in a fairly prominent location in town and I would pass it daily not paying much attention to the university crest and 1413 – 2013 etched into the window (now sadly gone thanks to some nerd who broke the window). The 600 year celebrations started a couple of years ago in that teaching started before 1413 but it didn’t receive the Papal Bull until then. Hence the reason why academic parents could always find a mistake in a bejant or bejantine’s Raisin receipt.

One of the many traditions at the university is that of academic families and dates back to the time when the student’s staple diet was oatmeal and salt herring which is probably much healthier than that of today! Senior students would adopt first year students, known as bejants, to ensure that they settled in and had someone that they could turn to if in difficulties. This culminated in Raisin weekend which takes place in early November and, as a thank you, the bejant gave their “in loco parentis” a pound of raisins (a luxury food item) to supplement their meagre diet. It is nowadays, sadly, just an excuse for an alcohol fuelled binge, so much so that their disgraceful antics this year were picked up on by some of the national dailies. In my time as a student, 1975-1982, there was a fair amount of alcohol involved but not to the excesses seen today. Perhaps this has something to do with the fact that student numbers have more than doubled to 7500. Back then, on the Sunday, the first years attended a tea party given by their academic mother(s) and gave a gift of a bottle of wine and in return they got a Raisin receipt written in Latin, dated from the founding of the university and could be on anything. In addition they would get a Raisin string made from the tassels from their academic mother’s mortar board – 3 colours denoted the mother was a 3rd year student (Tertian) and 4 colours a 4th year student (Magistrand). An apt gift would be attached to the string and the student would attach it to their scarlet gown. Their academic father(s) collected them from the tea party (they too would receive a bottle containing something of an alcoholic nature)and take them to a local hostelry or hostelries in order to get them well and truly drunk as they would need to be for what happened on the Monday! They would receive another receipt from their academic father(s) as well. On the Monday, they attended lectures accompanied by their receipt(s) and then gathered in the Quad at 11am for what is now a foam fight/party. If you could find a mistake in the receipt then the student had to sing the first verse of The Gaudie and since there was uncertainty in the date of the founding you could always argue that their date was wrong! If they failed in their attempt to sing The Gaudie then they could be flung in the harbour or the fountain in Market Street which is now filled in and used as a flower bed. Hence you needed to know The Gaudie! It is a sight to behold with many shivering students on a November morning wearing, in some cases, next to nothing, carrying buckets of horse manure and other assorted items!

Listener 4270-1
It was in December last year when I came up with the idea of celebrating the University of St Andrews’ 600th anniversary, the third oldest university in the English speaking world and the oldest in Scotland. For people who don’t know, St Andrews is in Fife and if you look at a map of Fife it looks like the head of a Scottie dog and St Andrews is at the eye! Perhaps by passing the university shop on a daily basis a subliminal message had finally got through to my thick head as I’d been bereft of ideas for my next Listener puzzle given that my last one had been started some 15 years previously.

Solvers who remember Tough Crosswords may recall that the mathematical puzzle in issue 2 was one of mine entitled ST ANDREW. In that puzzle, which had a cross as a grid, the letters represented prime numbers less than 100 and had upper and lower case letters. Furthermore, in some clues, only the last 2 or 3 digits of the answer had to be entered as they were prime powers of primes.

I decided to revisit this idea but this time the prime numbers would sum to 600. To cut things down a bit I opted for 2-digit prime numbers only. As my son had just returned for the Christmas holidays from Strathclyde University where he is doing Electronic Systems and Computing, I asked him to write a program to find all the possible solutions. This he achieved with a few lines of Java – I, of course, would have used Basic! There were only 5 solutions and if I’d thought about it I could have found them quite quickly by hand!

I 41 67 71 73 79 83 89 97
II 47 61 71 73 79 83 89 97
III 53 59 67 73 79 83 89 97
IV 53 61 67 71 79 83 89 97
V 59 61 67 71 73 83 89 97

 
Listener 4270-2I chose the third set and got to work. I toyed with using a cross as a grid again but decided against it on the grounds of entry length and ugliness, so went for a portrait rectangular grid instead. I intended to have the dates appearing only on the main diagonals as an elongated knight’s move and all the pictures I’d seen were of Andrew and a portrait cross on which he was crucified, not a landscape one. By the end of the Christmas holidays and with most of the grid filled in I looked at the clues I’d written and decided to start all over again as they were just rubbish. I had eight fairly helpful letters to use to write clues unlike last year’s puzzle 2x2x2 and hadn’t used them to any good effect.

I had to postpone the resetting until after our S5/6 prelims in January and so it was in February that I got started on it again. I took this chance to rebar the grid and have the dates appear unclued at the top and bottom with the diagonals confirming them instead. I also changed to the rather obvious first set as I wanted A to be a prime ending in 1 and the primes in order would spell out ST ANDREW. Of course I could have used set II but I didn’t. These dates were put in first along with the 8-digit entries and I was particularly pleased with SWAT NERD as it is something I’d quite happily do to those students whose antics have sullied the university’s good name and reputation. Now to set the way in by using 23ac/15dn which was to use S and AS with the last digit checked and would force A to end in 1. Then 12dn/18ac that fixed A = 71. With only 8 letter/number assignments to find, albeit from one of five sets, makes the solving process reasonably straightforward. I set 5ac as E – A + T but then remembered Shirley’s penchant for clues that have something to do with drink so changed it round to T + E – A with apologies for not having something a tad stronger!

I had a list for all the ‘power of’ possibilities and decided to be kind and have them all fully checked bar one that would require just the last digit to be found. Since we are dealing with integers the unit’s digit of the answer only depends on the unit’s digits of the numbers being multiplied together. In this case it is the same number being multiplied by itself over and over again. This yields the following table.

Unit digit Unit digit of
the powers
0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1
2 2 4 8 6 2 4 8 6
3 3 9 7 1 3 9 7 1
4 4 6 4 6 4 6 4 6
5 5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6 6
7 7 9 3 1 7 9 3 1
8 8 4 2 6 8 4 2 6
9 9 1 9 1 9 1 9 1

 
So we have an exercise in pattern spotting. If the base number ends in 0, 1, 5 or 6 then the unit’s digit will always be 0, 1, 5 or 6 respectively. In the case of 4 and 9 the last digit oscillates between 2 possibilities depending on whether the index is odd or even. The remaining digits 2, 3, 7 and 8 have cycles of 4 digits and so to find the desired digit you only need to divide the power by 4 and note the remainder. A remainder of 1 is the 1st number in the cycle, a remainder of 2 is the 2nd digit in the cycle, a remainder of 3 the 3rd digit and a remainder of 0 the 4th digit. Choosing a base number which ended in 1 or 9 was out as the answer for the former is always 1 and for the latter 9 as the power would be odd.

This is something well within the grasp of a bright 15 year old and since my credit class last year which I’d had for their two year course (S3/4) could do it I reckoned that solvers would rise to the challenge. No need for fancy notation or high powered maths (no pun intended). Incidentally two thirds of them had also been in my first year class and such was their enthusiasm for Tony Gardiner’s resource the 26 Statements that it inspired me to set Elementary Number Theory [Listener 4125] so you now know who to blame for that puzzle – a lot of very bright and able pupils, all of whom got their Credit maths this year!!

I knew full well that some solvers with Mathematica or Derive would just type in 73^71 and obtain the full answer of 1976619468344396081886594006474396844766256166675285816488083771595943270654277610802483648808808660136266507145917734994994406091577 in microseconds. Solvers who use the web could have gone to the Wolfram Alpha site and typed in 73^71 and got the same result. However, as always, this wasn’t necessary.

I sent it off to Shane with the plea that hopefully it could be published this year. The May slot had already been scheduled and, by the time things were being finalised, the August slot had gone too. I did wonder if Roger would move the puzzle to St Andrew’s Day which was a Saturday and was pleased to see that we were on the same wavelength but for a completely different reason. In fact, such is the power of the Listener editors, they can influence a national broadcaster to air programmes related to the theme of their current puzzles on the day in question – Dr Who on BBC1 and Ever To Excel on BBC2.

As I look back on it now, I can’t help feeling that perhaps I ought to have contacted Phi, another of the university’s alumni, about the prospect of setting a joint puzzle. What would his clues have been for Bejantine or Raisin Receipt I wonder? Isn’t hindsight a wonderful thing?

Aien Aristeuein

Oyler

P.S. I hope that a St Andrews graduate won at least one of the prizes!
 

Advertisements

3 Responses to “Listener 4270, Alma Mater: A Setter’s Blog by Oyler”

  1. Thank you Dr C, another great puzzle! Although my ‘way in’ differed very much from your ideal one…

  2. Dr C said

    You always were different Finlay!! Awrabest and good luck.

  3. 76Clifford said

    Hello admin, i must say you have high quality articles here.
    Your blog should go viral. You need initial traffic boost only.
    How to get it? Search for; Mertiso’s tips go viral

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

 
%d bloggers like this: