OK it's time for a curiously counter-intuitive conundrum! It's called the Monty Hall problem when it appears in The Curious Incident of the Dog in the Night-time (a favourite book of mine!), and has also featured in different guises elsewhere. In this version....

You are on a TV Game Show. You have the chance to win a car....or a goat. There are three doors in front of you. You are told that behind two of the doors there is a goat, and behind the other there is a car. If you open the correct door you get to keep the car (you would prefer the car!).

But first, the Gameshow host invites you to choose one of the three doors, tell him which one it is, but not to open it. He then opens one of the other two doors, to reveal a goat (he can see what is inside each door and will always open one with a goat in). You can then choose to open one of the two closed doors. The question is, should you stick to your original choice, or change to the other door?

Qu'en pensez vous?

...the divisor problem. John told me a friend of his thought it could be 8,9. If this was so, the 'number' would be 4620, and the question states it is less than 4000. Here's why it isn't 8,9:

The LCM of 2 to 12 is 27720 (taking the highest powers of each prime factor). We can knock out 7 and 8 by dividing the LCM by 7 and then by 2, without affecting any of the other numbers. This leaves 27720 / 7 / 2 =1980, the solution (Sorry there was an error on the 'answer sheet' I posted!)

To remove 8 and 9 we would have to take out prime factors 2 and 3 from the LCM, giving 27720 / 2 / 3 = 4620 > 4000. Take out any more prime factors and you will eliminate more numbers from the divisors.

Hope this helps...if not wait for the next problem. It will be the Monty Hall problem as explained in The Curious Incident of the Dog in the Night-time.

Here is a solution to the divisor problem.

Forgot to put in a maths problem - how about this:

I'm thinking of a number less than 4000. It is divisible by all the whole numbers from 2 to 12 inclusive, except for two of them, which are consecutive. What is the number?

It's just been too long since I posted so probably everyone's given up reading my blog (sorry to both of you....). As for the Maths, I'm just tutoring A-level and GCSE at the moment; enjoyed brushing up my C3 and C4 (Pure Maths), and a bit of a crash course in D1 (Decision Maths)...! Also helping a young lad with preparation for scholarship to a top public school - which is surprisingly challenging as every question has an unusual twist to it!

Francais...en fin Mai nous allons en France pour le mariage d'un ami, qui prend place a une maison communautaire de la Communaute du Chemin Neuf (Tigery). Il est africain, elle est francaise. Il y aura beaucoup de personnes la, venant d'un peu partout. Je posterai tout de suite apres, avec des photos!

Music - since I last posted I've spent a lot of time learning the Pathetique Sonata, and a Chopin Etude in C minor with a crazy left hand. Also while clearing out some old stuff came across some cassettes with some of my favoutites from 30 years ago - Fats Waller, Barry White (!) and Diana Ross and Marvin Gaye. Memory lane.

The other day, as John mentioned on his blog, we went on a family bike ride along the canal which was thoroughly enjoyable and totally healthy!

The post below has pictures from John and Katy's wedding!!!

First of all I want be sad and mention two of my favourite chords. The first is E7b9 (well not E in particular, it could be C or anything...). It comes in Cole Porter's "So in Love" (strange dear, but true dear) and it is very haunting! I also noticed it in Uptown Girl as a 'substitution' for G7, and in lots of 'jazzy' harmonies.

The next is usually written as F/G ie. F with a G bass, but it is really G11 (ie. G7,9,11) and it sounds great especially if you play it as GFG (left hand) CDFAC (right hand).

Next - French. I love those cheeky French words which are 'argot' but not rude - see if you know what these are: (not sure of the spelling)

C'est un mec costaud.
Ta bidouille est carrement chiade!
La bagnolle etait completement esquintee.

And finally, most importantly, news of the wedding of the year - John and Katy! It was simply fantastic from start to finish! Here's a piccy:

Well I can't believe nobody has solved the triangle puzzle - I know of at least 3 people who have "tried it" and given up. Apparently every primary school teacher in France can do it, since it appeared in the entrance paper to get into (primary) teacher training in a French University! So have a nother go - all you need to know is the formula for the area of a triangle (1/2 base times height).

Shakespeare??? - what's wrong with me, I thought I didn't like the bard! We went to A Comedy of Errors, starring Helen Martin (!) and it was one of the best, most entertaining plays I have Ever Seen in my Life!! A plot and characters which make Brian Rix seem straightforward; brilliant acting (especially by Helen need I add): after it finished I wanted to see the whole thing again. Did I mention how good Helen was? Her character leapt out from the stage, and had us alternately squirming and in stitches. I love Shakespeare all of a sudden! And there's more - I've just watched the film of "Much Ado about Nothing" with Emma Thompson, Denzel Washington, Richard Briers et al and thoroughly enjoyed that too!

The musical event of the month was going to see Bach's B minor Mass at the Sheldonian in Oxford on Saturday with Chris and our old friends Keith and Tonie. Keith is a highly analytic retired university lecturer who absolutely loves Bach. Not surprising as Bach must be the ultimate "Maths and Music". It was marvellous to hear this work live, having only heard it on CD before. Genuine old instruments including trumpets that looked like they were from a museum; a curly-wurly precursor to the souzaphone (about nine coils); a double-bass with 6 strings; a thin sounding old violin and a lovely cello which could be nearly as venerable as Lowri's! We were right at the front, just metres away from the soloists, which was rather exciting; the most extraordinary was the counter-tenor James Bowman who managed to make the [usually odd-sounding] voice sound authentic, rich and voluminous! At the end we mused as to whether this fulfilled our Sunday obligation; Keith thought it was worth at least 5 or 6!




So, here's a bit of Maths for you: