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'[OT] Integer Math with component elimination'
2006\03\10@043521 by

i'm looking for integer math formulas, dealing with a hand full of
components, but 1 of the components has no influence on the result:

i.e. the values A, B, C, D and E are used within the formula, but only
the value of A, B, C and D has influence on the result, while the E may
be any value, without changing the result.

examples like (A+B+E+C+D-E) are a bit too simple, as you can see at a
first glance that E is eliminated.

thanx!

Buehler, Martin wrote:
> i'm looking for integer math formulas, dealing with a hand full of
> components, but 1 of the components has no influence on the result:
>
> i.e. the values A, B, C, D and E are used within the formula, but only
> the value of A, B, C and D has influence on the result, while the E may
> be any value, without changing the result.
>
> examples like (A+B+E+C+D-E) are a bit too simple, as you can see at a
> first glance that E is eliminated.

So what's the question?

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
the question is to find some formulas, which look as they would require
the value 'E', but do not really need it.

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******************************

>{Original Message removed}
Buehler, Martin wrote:
> the question is to find some formulas, which look as they would require
> the value 'E', but do not really need it.

You're going to have to explain why.  Unless you can explain a good reason,
this looks too silly to spend time on.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
>> the question is to find some formulas, which look as they would
>> require
>> the value 'E', but do not really need it.

> You're going to have to explain why.  Unless you can explain a good
> reason,
> this looks too silly to spend time on.

So (I suggest) don't :-)
He, like you, as you oft times note, doesn't *have* to do anything
and, as you also note, needs not have anyone tell him that he does.
But I'll hazard a guess which may well be wrong but which indicates
that reasonable reasons may exist.

Guess / example:    A system is required to obfuscate the means by
which a process achieves its aims. By providing an algorithm with one
or more parameters which appear on 'reasonable inspection' to form a
part in the process, but which in fact have no effect on the computed
result, the user seeks to mislead would be system breakers. Further,
'data' which is provided to the system may in fact not affect the
computation per se but be part of a security or checking subsystem
which seeks to determine whether the system is being utilised
improperly.

Whatever.

eg

E = [(A^2-B^2)/(C^2+ 2.C.D + D^2)] x [(C+D)/(A-B)] x [ (C+D)/(A+B)] x
F

E will always equal F :-)

A, B, C, & D are all irrelevant to the result (except that certain
combinations are not allowed in order to prevent the result going to
infinity. eg A<>B, A <> -B, C <>D, C <> -D.)

The eg ratio of the parameters A...D to each other or their sums or
some other features may be set in some manner so that, while they do
not alter the fact that E = F , do indicate to a knowledgeable
inspector whether they have been set by someone who 'knows the rules'.

____________

Very vaguely similar real world example:        The last digit in your
VISA etc card number is a checksum which is derived in a complex but
computationally simple manner (so you can easily enough calculate it
mentally) from all the other digits, with the aim of determining
whether the card number can in fact be a valid one. It's intended use
is probably not so much to check correct data entry but to identify
simple minded fraud. A randomly generated number has one chance in 10
of being legitimate by this test.

RM

Math class assignment?  Some sort of quiz or contest?

I have a feeling that I know several ways to do what you ask but I want
to know why before I give an answer...

> {Original Message removed}
On Mar 10, 2006, at 1:35 AM, Buehler, Martin wrote:

> i'm looking for integer math formulas, dealing with a hand full of
> components, but 1 of the components has no influence on the result

Hmm.  Like the acceleration of an object in a gravitational field;
explaining why heavy objects and light objects fall at the same
speed ?

F = M1 A                general formula for motion

F = G*M1*M2 / R^2   gravitational force.

G*M1*M2/R^2 = M1*A      M1s will cancel out...

BillW

yes, you're right. it's for a quiz.

************************************************************************
******************************

>{Original Message removed}
On 3/10/06, Buehler, Martin <Martin.Buehlerkeymile.com> wrote:
>
> i'm looking for integer math formulas, dealing with a hand full of
> components, but 1 of the components has no influence on the result:
>
> i.e. the values A, B, C, D and E are used within the formula, but only
> the value of A, B, C and D has influence on the result, while the E may
> be any value, without changing the result.
>
> examples like (A+B+E+C+D-E) are a bit too simple, as you can see at a
> first glance that E is eliminated.

(x-a) * (x-b) * ... (x-z) = ?

Bill

--
Psst...  Hey, you... Buddy...  Want a kitten?  straycatblues.petfinder.org

>
> Very vaguely similar real world example:        The last digit in your
> VISA etc card number is a checksum which is derived in a complex but

The LUHN check was intended to guard against manual entry errors.
>
> Very vaguely similar real world example:        The last digit in your
> VISA etc card number is a checksum which is derived in a complex but

The LUHN check was intended to guard against manual entry errors.
Someone already mentioned that putting the same 'factor' in twice can
let you add/subtract or multiply/divide by the same value.

A+E-E = A so E is non-essential
(A*E)/E = A so E is non-essential but problematic if E == 0.

You can make the rest of it fairly arcane as long as you use opposing
operations through algebraic reduction.

(2*(4*A + B + 5*C + 3*E)) / (6*E)

> {Original Message removed}
Russell McMahon wrote:
> E = [(A^2-B^2)/(C^2+ 2.C.D + D^2)] x [(C+D)/(A-B)] x [ (C+D)/(A+B)] x
> F
>
> E will always equal F :-)
>
> A, B, C, & D are all irrelevant to the result (except that certain
> combinations are not allowed in order to prevent the result going to
> infinity. eg A<>B, A <> -B, C <>D, C <> -D.)
>
> The eg ratio of the parameters A...D to each other or their sums or
> some other features may be set in some manner so that, while they do
> not alter the fact that E = F , do indicate to a knowledgeable
> inspector whether they have been set by someone who 'knows the rules'.

But that could just as well have been implemented by simply checking A-D
according to some rules.  For example, you could require them to each be a
different hash function of F.  There is no need for them to take part in the
computation of the formula.  We assume that whoever is sending the values
can't see the algorithm, else of course they could circumvent it in either
case.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
Buehler, Martin wrote:
> yes, you're right. it's for a quiz.

Then you can make up anything, like adding a variable in one place and
subtracting it somewhere else.  I guess I still don't understand the
question.

Were you asked this in a quiz or are you trying to create a quiz to see if
the students are sharp enough to reduce out the irrelevant variables?

If the latter, my highschool physics teacher had a good one that got a bunch
of us going for a while.  Take a basketball and put a hoop around it that
just fits (hoop same diameter as ball).  Now add 4 inches in length to the
hoop.  If you keep the hoop circular, what is now the clearance between the
ball and the hoop?  He asked this in class, and we all dutifully computed
the answer, with most answers right.  Then just as we were leaving he said
to come back tomorrow with the answer to the same problem, but what if the
hoop now went around a sphere the size of the sun but you still only added 4
inches to it.  When I got home I cranked out the answer real quick, but I
kept getting the same answer as the basketball case and I could figure out
what I was doing wrong.  I didn't understand my error until next day in
class.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
Olin wrote regarding 'Re: [OT] Integer Math with component elimination' on Fri, Mar 10 at 12:07:
> If the latter, my highschool physics teacher had a good one that got a bunch
> of us going for a while.  Take a basketball and put a hoop around it that
> just fits (hoop same diameter as ball).  Now add 4 inches in length to the
> hoop.  If you keep the hoop circular, what is now the clearance between the
[...]

So, did your highschool geometry class cover things like simple
mechanics and Snell's law, since the geometry was being handled in
Physics? :)

--Danny

On Mar 10, 2006, at 10:22 AM, Danny Sauer wrote:

> did your highschool geometry class cover things like mechanics
> and Snell's law, since geometry was being handled in Physics?

Don't be snide.  For a brief moment of time in college, my
physics, calculus, and EE classes were all overlapping in
their coverage of matrix algebra/calculus (gradients?  I can't
even remember the terms :-()  It was WONDERFUL.  I wish school
was always like that, and I'm not convinced it shouldn't be.

BillW
>> Very vaguely similar real world example:        The last digit in
>> your
>> VISA etc card number is a checksum which is derived in a complex
>> but

> The LUHN check was intended to guard against manual entry errors.

But is sufficiently obscure in form that, while easily computed
mentally, would never have it's algorithm be discovered by mistake or
without determined analysis. Which points to it being meant to be a
bit "hidden" as well as being for data checking. Otherwise a more
direct modulo 10 sum would (I think, probably) be just as effective
and error immune. (ie - not very error immune as it uses only a single
digit with 10 choices.

RM

> Russell McMahon wrote:
>> E = [(A^2-B^2)/(C^2+ 2.C.D + D^2)] x [(C+D)/(A-B)] x [ (C+D)/(A+B)]
>> x
>> F
>>
>> E will always equal F :-)

> But that could just as well have been implemented by simply checking
> A-D
> according to some rules. ...

Indeed. I think the object is to include a parameter (in my case 4
parameters) in the algorithm but for it/them to have no effect on the
answer. I added the security part as a guess as to reason.

RM

William ChopsWestfield wrote:

>> did your highschool geometry class cover things like mechanics
>> and Snell's law, since geometry was being handled in Physics?
>
> Don't be snide.  For a brief moment of time in college, my
> physics, calculus, and EE classes were all overlapping in
> their coverage of matrix algebra/calculus (gradients?  I can't
> even remember the terms :-()  It was WONDERFUL.  I wish school
> was always like that, and I'm not convinced it shouldn't be.

I'm convinced it should be. Most people learn physics better in automobile
repair class (if they are interested in automobiles, that is :) and learn
math better in classes where math gets applied rather than treated for its
own sake.

Learning with a purpose is much more effective. I've given enough tutor
classes in math and physics in high school (or the German equivalent of it)
to have experience with why people "don't get it".

Gerhard

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