Tuesday, 15 December 2009

Do they know it's Christmas?

At a fairly seasonal time, I've been looking through some old quiz rounds that I've written, and particularly amusing myself with the OUQS Committee Quizzes, which were all about writing clever themed rounds. This is that I particularly enjoyed from Christmas 2005, I believe. If you were wondering, the theme was "Do they know it's Christmas?".

1. Many Orthodox churches, such as the Coptic and Russian Orthodox, will not know that it’s Christmas time on 25th December. What date do they celebrate Christmas?

2. Which Oxford Christian Society aims to make sure they know it’s Christmas time by annually announcing the date on which Christmas will fall?

3. Some Christian sects will not believe it’s Christmas time. Which group, possibly most noticeable for their rejection of blood transfusion, do not celebrate Christmas?

4. Other religions don’t quite accept that it is Christmas time, but that’s no reason not to celebrate. The Jewish festival of Hanukkah is celebrates the events described in which apocryphal book of the Bible?

5. Do we know when it’s Christmas time? How many days is it ‘til Christmas?

6. Does he know “Do They Know it’s Christmas Time?” What single surpassed “Do They Know it’s Christmas Time?” as the all time highest selling UK single in 1997?

7. You know when it’s Christmas time when repeats of old TV series start appearing. At the beginning the only Father Ted Christmas Special, Ted rescues a group of priests from the largest example of what in Ireland?

8. Do you know your Christmas Time? The twelve days of Christmas spans the time between Christmas Day and which other Christian Feast Day, celebrated on 6th January?

9. When you’ve known that it was Christmas Time, it’ll be Boxing Day, otherwise known as St. Stephen’s Day. The story of St Stephen is told in which book of the bible?

10. It doesn’t have to be Christmas time, but you know it’s my quiz when there’s a random piece of education about Belfast thrown into the quiz. What is the name of the Belfast Cathedral, outside which stands the famed “Black Santa”, who is the dean of the cathedral collecting money for charity throughout December?

Saturday, 12 December 2009

Half the fun is...

The last couple years have been good for travel from me, and being the sort of person that I am, planning the travel tends to be almost as fun as actually travelling! It'll come as little surprise that I was someone who used to play with maps and timetables when I was younger. That really is no joke...

Anyhow, I've come across a website that has made me, if it were possible, even more obsessed. It's called Tripit, which acts as a travel itinerary accumulator, so you make your bookings for flights, coaches, trains, hotels, activities and whatever, forward them on to Tripit and they sort it out so the itinerary is in one place. It's entirely possible that I'm one of the few people who could find this fun and exciting, but the itineraries made are quite cool, and in case anyone falls into the same personality type as me, I thought I'd share...

Friday, 11 December 2009

Beyond a joke. Literally.

Quite a popular joke that keeps being pushed in the faces of mathematics teachers is the following comment on the evolution of British mathematics teaching:
1. Teaching Maths In 1970
A logger sells a truckload of timber for £100.
His cost of production is 4/5 of the price.
What is his profit?

2. Teaching Maths In 1980
A logger sells a truckload of timber for £100.
His cost of production is 4/5 of the price, or £80.
What is his profit?

3. Teaching Maths In 1990
A logger sells a truckload of timber for £100.
His cost of production is £80.
Did he make a profit?

4. Teaching Maths In 2000
A logger sells a truckload of timber for £100.
His cost of production is £80 and his profit is £20.
Your assignment: Underline the number 20.

5. Teaching Maths In 2008
A logger cuts down a beautiful forest because he is selfish and
inconsiderate and cares nothing for the habitat of animals or the
preservation of our woodlands.
He does this so he can make a profit of £20.
What do you think of this way of making a living?
Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers. )
We can all have a laugh at this, safe in the knowledge that this is hyperbole, and that although worried at the direction, we can be confident it won't get this bad. Or so I thought, until this question from my top set Year 8 was pointed out to me,
A penguin is standing on an iceberg that is melting because of global warning. It now has a diameter of 6m.
(a) Calculate the area for the penguin to stand on.
(b) Where else could the penguin go to live?
Part (b) I'm sure will be enough for people to think that I've just pushed the joke that little bit beyond believability, but alas not, it really was there. I'm trying to assess whether that was better or worse than the question from a Year 7 textbook that, after a question on calculating the number of loyalty card points could be earned on purchase of bananas, genuinely asked the question,
(c) Do you like bananas?
I can't think why so many maths teachers lose confidence in the system...

Wednesday, 9 December 2009

The Machine is us/ing us

You can tell it's a quiet night - I've been looking through some old videos that I've enjoyed in the past, and came across this one. It's a pretty cool way of introducing what's really meant by "Web 2.0"


Negative Number Confusion

I feel that most people I tell about this article are starting to think that I'm spinning some sort of tale. Now admittedly, that's not massively unlike me, I'm quite happy to build up a lot of story around the telling of a simple joke, but for once this is really true - read this story from the Manchester Evening News all the way back from 2007.

My favourite quote has to be,
"I phoned Camelot and they fobbed me off with some story that -6 is higher - not lower - than -8 but I'm not having it."
but I must admit it wouldn't be half as funny if it didn't have a "I'm not having it" at the end. It's almost enough to make a maths teacher give up and go home...

Saturday, 10 October 2009

Have you heard the one about the statistician, the number theorist and the engineer?

My classes have been suffering from mathematical jokes. I feel I should spread them more widely...
A mathematician decides he wants to leave the mathematics trade and become a fireman, so he goes to the local fire department. "OK, then, let's see how you do in a little test," the fire chief says, "What would you do if you passed an alley and say there was a bin on fire?" "Well," replied the mathematician, "I'd get a hose, connect to an hydrant, and then pour water on until fire goes out." "Very good, but what would you do if there was no fire?"

The mathematician thinks for a bit, then says "Well, then I'd have to find a match and set the bin on fire." The fire chief nearly chokes, "Why on earth would you do that?" "It's obvious, it reduces it to a problem I've already solved..."
Boom, Boom! More on the computing end of things...
Why do mathematicians get Hallowe'en and Christmas confused?
Because for a mathematician, Oct 31 is the same as Dec 25!
And for the true geeks...
What's white, non-orientable and lives in the sea?
Möbius Dick
I'm here all week, just so you know...

Connecting with the Norn Irish in me

I live my life as an exile - I've now been living in England for some seven years and counting, with no prospect of returning to the motherland. As a result, I enjoy indulging in anything Northern Irish whenever it's presented to me. One of the avenues of this indulgence is the writings of John Pepper, a columnist for the Belfast Telegraph. I've been rereading his Illustrated Encyclopedia of Ulster Knowledge, which is hilarious in a "so true" sense for anyone from, or for that matter has visited, Northern Ireland. Take this entry under Exile:
"The Exile doesn't exist who fails to prick up his ears at the sound of a familiar accent far from home."
I remember times in Oxford when I had to be dragged away from people after a half hour conversation with a total stranger based solely on our common homeland. While there have been a number of laughs come from it, I'm feeling like getting a copy of it for my English friends, then they might have a fighting chance of understanding what I'm on about when I refer to scallion, sodas or start to talk about it being donkeys since we last did something...

Sunday, 4 October 2009

Mightier than the Waves

I have just returned from a weekend on the North Cornish coast with a few members of my small group from church. It was spectacular, and I feel that there may be a competitor for the North Antrim Coast as contender for favourite spot on earth. I'm hoping it won't be the last time I'm back! The photo on the right comes from the Bedruthan Steps near Mawgan Porth. We climbed down at high tide, and so the waters were surging right up to the bottom of the stone staircase, and looking a little ferocious. One of the people reminded me though of Psalm 93, which rather coincidentally was read out at church this evening:

The Lord reigns; he is robed in majesty;
the Lord is robed; he has put on strength as his belt.
Yes, the world is established; it shall never be moved.
Your throne is established from of old;
you are from everlasting.

The floods have lifted up, O Lord,
the floods have lifted up their voice;
the floods lift up their roaring.
Mightier than the thunders of many waters,
mightier than the waves of the sea,
the Lord on high is mighty!

Your decrees are very trustworthy;
holiness befits your house,
O Lord, forevermore.

From my perspective, these waves were pretty mighty! What an amazing God we serve! It's always nice when you experience something that allows you to appreciate such a truth anew.

Sunday, 27 September 2009

Doug Wilson on Calvin and the Bible

I've just finished listening to Doug Wilson's talk at the Desiring God conference, and would give it strong recommendation - particularly for it's strong defence of the role of preaching derived from the authority of God's word.

As a pleasant aside, the introduction gives a good reason for why we are happy to call ourselves "Calvinists", while at the same time refusing to venerate John Calvin beyond his role as a human teacher. In as such, the first ten minutes comes with particular recommendation for anyone who feels shy of the title, or is inclined to reject the need for human teachers altogether. Then by the time you've listened through that much, you may as well keep going...

Monday, 21 September 2009

Checkout Challenge

I was posed a question recently by a colleague at work, and on reflection I'm struggling to figure out why it hasn't been a bit of a chestnut on the quiz circuit, as it appears to have many of the qualities required. Or maybe it has been and I just haven't noticed. Anyway here it is:
What is the lowest checkout in darts that required a 3-dart finish?
For those uninitiated in the great sport of darts, a checkout needs to finish on a double or a bullseye (50 points). To count, it must require three darts, and not be able to be done on one or two darts, e.g. 40 wouldn't count, no matter how many times you insist you could do it 5, 15, double 10, as it's quite clear that double 20 would do.

Feel free to comment any solutions. The method that my colleague and I used to solve it demonstrates an interesting method of proof, so a follow up on solution should be expected, along with a little discourse on some area of mathematics, I should expect.

Wednesday, 2 September 2009

Other Aspects of the Covenant

One thing I’ve been thinking about recently is the fact that being in the covenant isn’t necessarily good news. I feel I’ll need to elaborate on that a bit more - one of the passages that has been in my head is this one:

Woe to you, Chorazin! Woe to you, Bethsaida! For if the mighty works done in you had been done in Tyre and Sidon, they would have repented long ago in sackcloth and ashes. But I tell you, it will be more bearable on the day of judgment for Tyre and Sidon than for you.”

Matthew 11:21-22

The reason for woe here is the privilege that these two cities possess. They have seen the work of the Messiah, witness the signs that he points to, and yet have not repented, and because of that their judgement will be worse than that of Tyre and Sidon. For although the cities of Tyre and Sidon may well be ‘worse’, they didn’t get to see God at work in the flesh. In one way of putting it, it’s expected of Tyre and Sidon, they knew no better (although it’s worth noting that this fact doesn’t mean they escape judgement), but for Chorazin and Bethsaida, what were they thinking? They knew better than to reject God, and yet did so anyway and will be judged more harshly because of their knowledge.


The basic point is one that is almost self-evident: To be privileged brings additional responsibility, and although the passage above isn’t explicitly covenantal, there are many places where the same point is made. The biggest example would be the the people of Israel in the Old Testament. The curses for disobedience of Deuteronomy 29 are part of the covenant Israel had with God, and not in spite of it; they would be judged specifically because of their knowledge of God’s law. Another helpful illustration is that of another God instituted covenant relationship: marriage. To quote something I’ve been reading recently:

“The unfaithful man remains a husband – even though he has a slept with Suzy, Sally, Shirley et al. The fact such a man is a husband compounds the guilt; it does not lessen it in any way. If we knew that a man was promiscuous, and then found out he was married, we wouldn’t say, “Well, at least he’s married!” His covenant vows make his sin worse. When a single man sleeps around his sin is great. [...] When a married man is sexually treacherous, his sin is multiplied many times over.”

Doug Wilson, A Primer on Worship and Reformation

The same must be true in the New Covenant. There are those who have entered, through baptism, into a covenantal relationship with God, and then openly rebel and teach falsehood about the God with whom they have a relationship with. They are in the privileged position of hearing God’s word, and yet turning their backs on Him. The temptation of many evangelicals is to label these people as not Christians, but to do so is to let them off the hook. For a non-Christian to deny the deity of Christ is sinful, but understandable, but for a covenant member to say the same thing is to place themselves in far greater condemnation. To people who profess the name of Christian but live in disregard to God, the covenant is no place of blessing, but will stand in judgement against them. And so there must be an urgency in trying to win our brothers over, by having a view of them both as brothers within the same covenant and as those facing judgement because of their evil, and we will do so by acknowledging the issue as one of church discipline rather than the more external one as it is presently currently conceived.

Returning to the Ether

It has been a long absence from the blogsphere, but I now endeavour to return. I shall attempt to place a few more thoughts up here from time to time, and shall also return to updating my Twitter a little more frequently (which at the time of writing, still claims that I have not reached Moscow yet. There is possibly more than one way that that's now wrong...).

Monday, 2 March 2009

Casting pearls before swine

At church, we've been looking at the Sermon on the Mount for a few weeks, and last night came the turn of the challenging passage of Matthew 7 and the passage about "judge not lest ye be judged". Without going into too much about the personal challenge of the passage (for those interested, you can listen to the sermon here), the main thrust was that passage was not an excuse to not challenge ungodly behaviour in fellow Christians, but rather to correct others with humility and an awareness of your own sin. In the context, we came across the somewhat puzzling passage of Matthew 7:6:
"Do not give dogs what is sacred; do not throw your pearls to pigs. If you do, they may trample them under their feet, and then turn and tear you to pieces."
Now in the context of the encouragement to humbly correct our fellow Christians, the way that this verse was thought about was that sometimes we will correct others in all humility but still find it taken badly, so the encouragement is not to lose heart in humble correction to be the right thing to do. Now this makes a lot of sense, but I still feel a little uncomfortable about it - firstly, Jesus' words seem to read as an endorsement not to even try something, rather than an encouragement for those who have had bad experiences trying to do the right thing, and secondly the wording seems a little strong, after all reference to pigs doesn't tend to be made lightly.

With these in mind, an alternative suggestion was floated in small group afterwards, that the pearl might be alluding to the "pearl of great price" of Matthew 13:45-46, and so might be the gospel. This interpretation would say don't preach the gospel (the pearl) to non-Christians who have consistently rejected it (the pigs or dogs). This has the appeal that it is allowing scripture to interpret scripture, but this still seems to not fit right. The result of this might lead to a withdrawal of any hope of grace on certain people, that there are some people that we might be led to feel are beyond the call of the gospel and so we needn't bother preaching it to them, which might be right but feels wrong somehow.

I was therefore continuing to mull this through my head this morning, and my thoughts were returned to thinking of some comments N.T. Wright had made at a sermon in Oxford last year, which encouraged me to look back at the other "pearl" passage in Matthew:
"Again, the kingdom of heaven is like a merchant looking for fine pearls. When he found one of great value, he went away and sold everything he had and bought it."
Matthew 13:46-47
It seems that the pearl of great price isn't quite the gospel, but the "kingdom of heaven". Now the kingdom of heaven is a reference, I think, not only to the future rule of Christ that will happen when all things have been completed, but also his influence and rule on earth now. Elsewhere in Matthew (such as 4:23, 24:14), the gospel is referred to as "the gospel of the kingdom" or "the Good news of the kingdom". This would suggest that the thing of value isn't the gospel as such, but rather that the gospel is such good news because it declares the kingdom of heaven and God's rule to be available through the death and resurrection of Jesus Christ.

So how does that affect Matthew 7:6? Well, if the pearl is the kingdom of heaven, or to use different language, the rule of Christ, then we need to be careful in how we approach moral issues with non-Christians. With Christians who have strayed, it is wise to approach in humility to encourage one's brother (and also oneself) to submit their live more in line with God's word. But this approach is because you and your brother have sold all for the pearl of great price, and appreciate to some degree the greatness of Christ's rule. To take a similar line with non-Christians won't work, they scoff at God's rule, so why cast our pearls in front of them to convince them? Rather, we need to proclaim the beauty of the pearl itself, and hope that God opens their eyes to appreciate the pearl themselves.

To clarify, I'm not saying that non-Christians are necessarily unpersuaded to live God's way in some areas, but rather to try and convince them to adapt to some moral solely because it is God's will is misguided, and we rather need to address the core problem of rebellion to God before focusing of living lives according to the will of God.

Sunday, 1 March 2009

Maybe short is more my style...

I think I'm going to experiment more with Twitter, we shall see if that gets update more than this blog does!

(That said, I shalln't be ignoring here, not that I'm particularly active...)

Saturday, 21 February 2009

Colour in black and white

This is quite a cool optical illusion thing, worth checking out.

Thursday, 19 February 2009

Consolidation

For anyone who might notice these sort of things, I've imported a few posts from a previous blog that I used to keep, just to bring most of the stuff that I write together in one place. This would be why there are some posts that seem to come before the post that gives an introduction to the blog.

Of course, I write this and the most likely outcome is that no-one notices anyway. And yet I keep writing...

Reading for Relaxation

One other notable point that occurred during my trip away: I have now read my first P.G. Wodehouse. I had been strongly recommended to try something from him, and so whenever I was in second hand bookshops, I always had a quick look to see if I could pick anything up. It's a testament to his popularity, I suppose, that his books seem to be quite rare, but I did finally find a copy of Ring for Jeeves in the Blackwell's second hand section. 

I'm pleased to say I quite enjoyed it, and I think I've found a pleasant source of fairly lightweight reading (in the best sense of the term, as in not too heavy when you are looking for a little revival). The humour seems to be quite similar to that of Jerome K. Jerome, that I had the pleasure of sampling near the end of last year - rather focused on the charmingly absent minded. It does, however, make for embarrassment in public reading, randomly laughing out loud on a train is not considered the done thing in Britain...

I'm now back into the cycle for the reading group that I attend, after missing a couple of meetings, first due to illness then down to not hearing which book early enough to read it in time. The book this month is Nada by Carmen Laforet, a translation from Spanish about a teenager coming to study in Barcelona in the years after the Spanish Civil War. Quite a change in tone from my holiday reading, but the first few chapters seem promising, and shall be nice to be able to join a discussion again.

Wednesday, 18 February 2009

Wonderful Copenhagen

I'm now back from a very pleasant few days in and around Copenhagen on my half-term holidays. It's quite a wonderful place, and I'm already making mental plans for a return, maybe in the summer for a bit of a cycling tour. It was very cold, as I suppose one should expect if one visits Scandinavia in February, but although I'd like to return when it was a bit warmer, the cold does allow it to snow which added something to the place. It has quite a fairy-tale sort of feel to it in normal weather, but the snow made the old town look like the sort of scene you'd expect to see illustrated in a story book. It's not hard to see where Hans Christian Anderson got much of his inspiration from!

Other highlights of my short break include: walking around Hamlet's Elsinore Castle in the freezing cold and snow, lots of time to relax and read, lovely roommates in the hostel and ensuing evening conversations about home countries and the like, finding somewhere suitable to watch Ireland move one step closer to a first Six Nations trophy, finding a horse stable in the Carlsberg brewery and intrepid voyages decided over a cup of coffee while assessing one's options. A successful few days, me thinks.

It all has to end and it sometimes does so in a thump, as in this case. Tomorrow is the day decided for returning to school to plan lessons for the new term. Sigh.

Sunday, 8 February 2009

Caution: Mathematician Unwinding...

As much as I love the jaunt into Oxford, I'm always left exhausted at the end of it, so this evening has primarily consisted of collapsing and not doing much. What has been my entertainment? Well, as a clue:
"We all use math everyday, to predict weather, to tell time, to handle money. Math is more than formulas and equations: it's logic, it's rationality, it's using your mind to solve the biggest mysteries we know."
Oh yeah. I love it, or at least I would love it more if it learnt that it's not math, it's maths (or maybe it's maz. Maybe I'm not the best one to point out the pronunciation here...)

The purpose of baptism

I've just returned from Oxford, where I spend a little time in the company of Doug Wilson, including hearing him speak at a talk addressing the misconceptions that surround the Federal Vision. These talks were rather helpful, and have given some food for thought, but one question that I want to mention, although not at this point answer, is the following:
If we believe that we are saved entirely through faith alone (which I do), what purpose is there in baptism?
That is to say, is it the case that we either accept the first clause (we are saved sola fides) and therefore could replace baptism by a public confession (or at least would simply have to retain baptism just to be obedient for obedience sake, which is not necessarily a bad concept), and the alternative is to reject sola fides and turn baptism into a ritual which either has to be completed as part of salvation or indeed brings salvation in and of itself.

It is easy to guess that I am beginning to feel that the above option do not comprise a complete set, and indeed that there are alternative ways of thinking, but as I said, I am not planning to answer my question now, I simply leave it as a place holder for future thinking. Be assured that although my fingers are not yet working on this topic, the cogs of my thoughts have begun to turn on the issue...

Thursday, 5 February 2009

So the snow dance was the problem...

Finally!

The good news came on BBC Bristol this morning. As it is, I'm now writing this in bed...

Wednesday, 4 February 2009

Really? I hadn't noticed!

You know, for all the talk I make about how silly and annoying pupils are for pointing out the bleeding obvious during lessons, as in "Sir, it's snowing!", the BBC News website top story for most the last week has had a similar inclination. 

But then again, so has this blog. There's another severe weather warning for this evening. I'm putting away the snow dance, accepting the fact that it's a useless device. Still, here's hoping...

Monday, 2 February 2009

Sir, sir, it's snowing!

Further to yesterday's post, snow did not happen in time and I went in as normal. Except it was the worst of two worlds, seeing that it was snowing (leading to kids generally spending more time looking out the window that listening to my lesson), but not enough to get time off work. Drat. To look for silver linings though, I did indeed not stay up for the Superbowl, but even then it appears I missed another classic. Maybe it'll snow in a sensible fashion for next year...

Still, BBC weather forecasts heavy snow for this evening and the Met Office is putting at 60% chance, so the snow dance continues. 

Sunday, 1 February 2009

Doing the snow dance...

It's cold and there is snow predicted this evening. Now if only I could ensure that tomorrow was a snowday, then I'd be able to stay up and watch the Superbowl...

I'm really not going to take that chance though. It's a tough, tough couple weeks ahead and I'm predicting a perfectly natural sleep debt without adding to it from my own stupidity...

Saturday, 31 January 2009

The numbers behind the music

I've spent this morning tutoring at a Year 8 Mathematics Masterclass on "Mathematics and Music", for which I have to admit to only having competency in one half thereof, but in spite of that it was very interesting. Towards the end of the lecture, my attention was drawn to the existence of the Fibonacci Waltz, a composition based on the Fibonacci sequence of numbers. How it is composed is by assigning a note to each number, so 1 is C, 2 is D and so on. Sharps are not considered for the purpose of this (although if someone wishes to attempt further composition...), and similarly octaves are disregarded so number 8 corresponds back to C, essentially meaning running the Fibonacci sequence in a form of modular 7 arithmetic. 

There are a couple of surprises in this piece, the first of which is that it is somewhat aesthetically pleasing! Mathematically though, I was surprised to see that it has a repeating sequence of 16 notes, and I'm now rather keen to see why. For a start, I would have probably expected the repeat to be some multiple of 7. Further to that, would the sequence repeat if sharps were included (turning it into a form of mod 11 arithmetic)? If it does, what about other modular bases? This is something that requires further investigation, I reckon, and I can already see an A-level class investigation brewing over this one...

Friday, 30 January 2009

The Great Wikipedia Race!

Introduced by the top set Year 11s and now the new craze in the staff room. A game for 2 or more players:

Each player logs on to a computer and goes to the Wikipedia homepage. Choose a destination article (such as Isaac Newton, Sydney Harbour Bridge, etc), then each player hits the "Random Article" button. The aim is then to navigate to the destination article as quickly as possibly by using only links found in the articles you are viewing, starting with the random article. 

Hours of amusement, and good use of the random tidbits and connections connected as a quizzer!

Oh yes, and I have indeed lost the game.

Thursday, 29 January 2009

The Path of Least Expectation

It's been a while since I've posted. This is due to finding out first hand that January is a rather long month in the teaching profession (typified by the question asked by one of the science teachers when he asked if I could come up with a mathematical explanation of why August never drags by January always does...), but for the sake of providing at least one post a month, I'll offer this poser...

I get quite annoyed when classes ask to change their seating plan, so my response to a question of "when are we changing the seating plan?" is "when you least expect it", pointing out that because they asked, they must have been, to some extent, expecting me to cave and allow it to happen that day. Now this is just to annoy them (hey, I'm allowed...), but here's the thought:

If I'd said to them instead, "Sometime this term, but when you don't expect it.", would there be a time available in the term to change the seating plan? To demonstrate this, imagine that we got to the last lesson of term and I still hadn't changed the seating plan. In this case, to keep my word, I would have to change the seating plan. But the pupils, if they remembered my original statement, would be expecting it, because it would be my last chance so I wouldn't have fulfilled the condition in my statement. Now, think if I got to the second last lesson. In this instance, because I know the pupils would have to expect my change if I left it to the last lesson, and so to avoid my pupils' expectation I would have to change it this lesson. Of course, I teach some bright cookies, and they too would figure this out in the second last lesson.

This logical process can be applied to every lesson of the term by continuing the iteration to the third from last, fourth from last and so on, so my pupils have to resign themselves to the fact that I simply can't fulfil my statement and the seating plan seems doomed to stay. Or does it? Is there a flaw in the logic, and why/why not?