Firstly an apology. In my message yesterday I may inadvertantly have given the impression of belittling Wiilem Bouman's ability to name the four consecutive prime factors of a sixteen digit number. This was not my intention and I do not wish this to be perceived as such.

I have realised in the meantime that there are other forms of (relatively simple) calculating operations which remain to be 'mastered'. For instance, there are the 'ratio calculations' which were introduced into competitive calculating in the World Cup of 2004. The basic idea is that a problem is rpesented in the manner of "A:B = C:D", with three of the numbers being given and the other needing to be identified. This is essentially a multiplication/division combination.

An alternative form of problem is one of my own device. 'Bracketed equations' can employ memory, but other techniques can be used in order to side-step this requirement. Here's the basic idea: Two sets of brackets are presented, each containing two numbers to be added together. Once these operations have been performed, the two results are multiplied to give the final result. An example: (15 + 29) x (31 + 14). 15+29=44, 31+14=45, and 44x45=1980. The final answer to the problem is thus 1980. These problems are smiple enough at the level I have given here, but they are not so simple when the numbers have four digits each.

Any comments/opinions?

Regards

George

--- On Wed, 10/9/08, George Lane <george972453@...> wrote:

From: George Lane <george972453@...>

Subject: Re: [Mental Calculation] Specialties

To: MentalCalculation@yahoogroups.com

Date: Wednesday, 10 September, 2008, 4:43 PM

Hi folks,

I'm not sure I'd say I've mastered huge division problems, but integer divisions aren't really too tough to handle. Remainders - the integer division problems with inexact results - are much more complex as the technique of performing the main division 'from the wrong end' is unavailable. Personally, I find remainders problems with sizes of anything in excess of 12/6 digits quite horrendous.

Prime factorisation without advance knowledge of consecutive prime numbers is something which may still stand to be 'conquered'. The problems of this kind are, essentially, long sequences of exact integer divisions in which the divisors need to be identified and the results remembered for the next division. The problems we face in the World Championships are not strong; the hardest in this year's event was a five-digit number with six prime factors. Hardly the challenge of giants. My 'Pegasus' training file presents numbers with 12 digits and which may have upwards of 20 prime factors.

I don't think the 'gimmick' operations (such as finding the 13th root of a 200-digit number) are really worth mastering; they have no relation to genuine mathematical requirements and seem to diminish a reputation rather than enhance it - bearing in mind there is little or no use for such operations in the real world.

Regards,

George Lane

--- On Wed, 10/9/08, A.W.A.P. Bouman <awap.bouman@ casema.nl> wrote:

From: A.W.A.P. Bouman <awap.bouman@ casema.nl>

Subject: Re: [Mental Calculation] Specialties

To: MentalCalculation@ yahoogroups. com

Date: Wednesday, 10 September, 2008, 1:26 PM

Dear Jsh,

You should have heard me laughing, I still do!!!!

I am honoured a little bit too much: it is factorising a 16 digit number composed by 4 consecutive prime numbers.

Don't worrie: there will always be something to conquer

George Lane can do huge divisions, I like to confirm that, nevertheless I doubt whether Rüdiger can do the same.

For me a very important criterium is versatility in operations. Therefore I give you some names of calculators not named in your message of which I personally could ascertain their versatility.

Alfabetically and surely not complete: Robert Fountain, Gert Mittring, Andrew Robertshaw.

As in a tournament always is a restriction in the total of operations it seems me to be impossible to conclude who is really the best of all.

For me it is very meaningful to be a part of the company of calculators, with whom I can interchange ideas, and that after 45 years "solitude in calcualtion" .

Regards,

Willem Bouman

----- Oorspronkelijk bericht -----

Van: jsh.flynn

Aan: MentalCalculation@ yahoogroups. com

Verzonden: woensdag 10 september 2008 11:32

Onderwerp: [Mental Calculation] Specialties

Dear calculating friends,

As far as I can see most skills have already been 'maxed out'

(dominated) by other mental calculators. For example:

Addition and multiplication: Alberto Coto (capable of adding 5 digits

per second)

Exponentiation: Ruediger Gamm (can raise any 2 digit number to any 2

digit power)

Division: I think Ruediger and George Lane have mastered this one.

Factorisation and logarithms: Willem Bouman (capable of factorising a

16 digit number! Also excellent at roots)

Calendar calculation: Jan and Matthias

So what is left to conquer?

Sincerely Jsh

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