So How does This Work Then ?

[AnOther]

http://www.regiftable.com/regiftingrobinpopup.html

[sid]

Looks impressive the first time!

The number you finish up with is always a multiple of 9, so you'll see that 9, 18, 27 36 etc all contain the same item, the one you're "imagining". It changes to a different item each time but always in the 9's multiple boxes.

Why 9? If you take the simplest example of a starting number of 10, the sum of the digits is 1, subtracted from 10 = 9. For every number greater than 10 you've added 1 to the sum of the digits but also increased the original number by, so you'll still get 9 when you subtract. I hope you followed that!

Edit: Hmmm! Not quite right, you don't always get 9, but a multiple of 9! For example 43 gives 36, so it's the next lower multiple. I'm sure a mthematician will give a more concise answer!

 

[PeterG]

[quote user="sid"]

Looks impressive the first time!

The number you finish up with is always a multiple of 9, so you'll see that 9, 18, 27 36 etc all contain the same item, the one you're "imagining". It changes to a different item each time but always in the 9's multiple boxes.

Why 9? If you take the simplest example of a starting number of 10, the sum of the digits is 1, subtracted from 10 = 9. For every number greater than 10 you've added 1 to the sum of the digits but also increased the original number by, so you'll still get 9 when you subtract. I hope you followed that!

Edit: Hmmm! Not quite right, you don't always get 9, but a multiple of 9! For example 43 gives 36, so it's the next lower multiple. I'm sure a mthematician will give a more concise answer!

 

[/quote]

 

You should try and get out more, Sid.........

 

 

[sid]

I do!

PS I'm from the Lancs/Yorks border too. No hope then. [:D]

[PeterG]

Which part?

[pachapapa]

In the days when engineers used slide rules, which were too complicated for bean-counters and Sinclair had still not started selling cheap calculators. Some mathematicians came to the help of the bean-counters and taught the bean-counters the basic principles of the "Extraction of Nines" ( not very difficult maths by the way, covered under the "Remainder Theorem" in the first year of "A" level maths). Wow! Eureka! A way of checking to an acceptable degree of probability the numbers in Double entry Book-keeping.

Of course prior, rich bean-counters were able to buy Marchant Electric Machines with cogs doing the nasty arithmetical operations; indeed the germans and the swedes made "portable" manual machines with cogs in them and not needing an electric plug; the Swedish name Facit comes to mind.

The "Extraction of Nines" is not mathematically rigorous and can give an error where for example a transposition of digits has inadvertently occurred. Not sure if the bean-counters were aware.

Today calculators are two a penny, but I note that when I deposit three checks with identical amounts, the bean-counter at Credit Agricole does three additions![:P]

[pachapapa]

When interviewing accountants I always used to broach the topic of casting out nines. A technique that I first came across in South Africa where it used to be applied to check land survey calculations using 7 figure trig tables in the field, called extraction of nines by folk there. There is also a slightly more difficult complementary technique known as casting out of elevens where positive and negative remainders are used. The method has the advantage that it will identify an error due to transposition of digits unlike the casting out of nines. A comparison comparing the two alternate methods in the link below.

http://mathforum.org/library/drmath/view/55805.html

 

[Iceni]

[quote user="pachapapa"]

In the days when engineers used slide rules, which were too complicated for bean-counters and Sinclair had still not started selling cheap calculators.

[/quote]

A "tool" that does not provide the answer may be acceptable for an engineer but not for an accountant. Before calculators were invented I used pencil, paper and brain.

Used to be an FCCA 

[pachapapa]

[quote user="Iceni"][quote user="pachapapa"]

In the days when engineers used slide rules, which were too complicated for bean-counters and Sinclair had still not started selling cheap calculators.

[/quote]

A "tool" that does not provide the answer may be acceptable for an engineer but not for an accountant. Before calculators were invented I used pencil, paper and brain.

Used to be an FCCA 

[/quote]

As a young accountant pre 1911 no doubt.[:-))]

http://192.220.96.166/articles/marchant/marchant.htm

[Kitty]

11,111,111 divided by 9 comes to 1234567.8

[Iceni]

Touché, PPP. It is so long since since I used a Marchant or even a (forwards/backwards) Facit that I had forgotten about them.

I met my first electronic calculator in 1968, a Canon Canola 16 (?), cost then £850 - more than my annual salary. Within 5 or 6 years the price of the cheapest Canon fell down through the £100 barrier and after another couple of years we were selling tiny little hand-held beasts at £5. Writing down the value of stock became a monthly task.

John

[pachapapa]

Now you got me reminiscing, I remember a pocket calculator that I used to in the early 50s; it had a metal stylus that one stuck into a hole in a sort of continous chain with numbers on it, if necessary it sort of went round the corner at the top and carried the tens digit forward. It was ok on addition and subtraction, when one subtracted there was a plate thing at the bottom which was elevated to allow a carrying down of tens. No idea what it was called.

[pachapapa]

Found it!!

http://www.flickr.com/photos/radiorover/2787677403/

Pocket Adding Machine
Screw the slide rule! I've got me a "New Pocket Adding Machine Adds & Subtracts".

[pachapapa]

Can you imagine checking in at JFK today with a CURTA in your hand baggage.[:-))]

[pachapapa]

As an engineer[;-)]I just have to post a UUUUy;

http://www.youtube.com/watch?v=HYsOi6L_Pw4&eurl=

[Chancer]

My sisters first job was as a comptometer operator for British Caledonian Airways, here were more comp operators in the comp room than there were typists in the typing pool, they mainly processed currency transactions and fuel and load calculations, she always used to lug the huge beast home with her at weekends but I never ever saw her use it, also she didnt seem to go to work very much and usually seemed to be on a jolly abroad using her flight concessions.

What I didnt know was that the woman in charge could have written the books "Completemente débordée!" or "bonjour paresse!" decades before the fonctionaires did, they maintained an illusion of being very busy and understaffed wheareas in fact they just chatted all day with half of them on watch randomly hitting the keys to make the expected noise, whenever anyone entered the office they would all join in, they had a rota system of who would be in the office and who would be shopping/at home/away on a long weekend, there were never however any empty desks as she simply employed more girls than they had desks.

The reason my sister always brought the behemoth home with her is that the supervisor did so well in creating this illusion of being overworked that they all had a least 12 hours overtime per week which they did (not) at home.

Then they all started getting very worried, the new pocket calculators threatened to replace the mechanical comptometer, they maintained the defence that the electronic calculators could not work to 12 significant figures like they claimed they did which bought the a stay of execution, then the chief bean counter bought one and found that by staying late for a couple of evenings he could do the work of the whole department and it finally dawned on him that they only actually worked to 6 significant figures.

[pachapapa]

A hinge point in my life was with RCM in 1972 when the Survey Office got their first delivery of HP-35 calculators, transcendentals, RPN, ROM  modules, etc ; a revolution. And an IBM 360 up the road at Research & Development.[geek]