Kiddie problem.

[mfgoode]

Originally Posted by xilman

Paul

Quote:
[Originally Posted by Tom Lehrer
Base eight is just like base ten really, if you're missing two fingers.] [/UNQUOTE]


I would call that a disadvantage in more ways than one!
e.g. ordering two beers from the bar maid not knowing the lingua franca eh Paul?
Mally

[mfgoode]

Originally Posted by mfgoode

[I am now of the opinion that I should lift the restriction of 3 digits to any finite number thus generalising the problem and making it more interesting.
Mally

Originally Posted by Wacky

I will even suggest that "125i" is not a number, but rather an expression. I do not consider it any more valid as "an answer" than is "125 X".

Be that as it may lets lift the restriction to any finite no. of digits by considering
125m : 25m : 5m.
[Note: BTW 25m is the G.M of 125m and 25m]



Thus by introducing an operator 'm' the ratio remains the same whatever the normal 'm' denotes whether it is an integer, +, -, *, i etc. on the set 125, 25, 5
Since these three no.s are in a fixed ratio of 5, whatever operation (multiplication or division) on the first must be similarly performed on the other two.

Take the controversial case of 0.125 , 0.025 ; 0.005

The original no.s are 125 , 25 , 5.

Dividing each by 1000 we get 125/1000 ; 25/1000 ; and 5/1000 thereby
getting 0.125 ; 0.025 and .005

Similarly with expressions such as 125i ; 25i ;5i and the rest of the other answers considered by us in previous posts including negative no.s.

I hope the above is clear and does not raise any more controversies.

Can you think of one more operation/expression that we have not considered before in this entire thread ?
Mally

[Wacky]

You make a good argument for the case that there is only one true answer, namely "125" and all of the other proposed "solutions" are just notational variations upon that answer.

[mfgoode]

Originally Posted by Wacky

You make a good argument for the case that there is only one true answer, namely "125" and all of the other proposed "solutions" are just notational variations upon that answer.

:surprised

[Quote=Wblipp]I was going to post solutions using a numbering system with a base other than 10. It was an interesting discovery that there are no such solutions. (i.e. no solutions in hexadecimal nor binary nor base-7 nor any other base.)
William]
In a way 'yes' richard but thanks for the observation.
William's full post if you refer to it is self explanatory for the answer.
Mally

[mfgoode]

Originally Posted by mfgoode/

Can you think of one more operation/expression that we have not considered before in this entire thread ?
Mally

:surprised
Since I got no more answers I am releasing the one that is left as I promised.
Hold your breath. It is
125! [factorial]
Any objections?
Mally

[Wacky]

Originally Posted by mfgoode

125! [factorial]
Any objections?

Yes, 5! : 25! : 125! are not a geometrical progression as was required in the original problem statement.

[mfgoode]

Originally Posted by Wacky

Yes, 5! : 25! : 125! are not a geometrical progression as was required in the original problem statement.

In our dogfight (aerial battles) Richard You seem to be trigger happy and right on my tail and I have no gunmen to back me up.
Yes the answer is not quite obvious at first sight but then appearances can be deceptive.
Still Im glad you noticed that as it stands its not a G.P.
Ill wait for a few more objections before I give my explanations which I hope
will be acceptable to you and the others.
mally

[mfgoode]

Originally Posted by mfgoode

Ill wait for a few more objections before I give my explanations which I hope
will be acceptable to you and the others.
mally

To all prospective candidates who intend answering this thread, positive or negatively, I will extend the dead line by one more day before I disclose the correct answer.
Kindly re-read the previous posts thoroughly as a lot depends on what you make out of them.
Mally

[mfgoode]

Okay heres my solution.
To reiterate, we started with the terms, 125 ,25 ,5.
Then we extended it to 125m , 25m , 5m where m denotes an interger/operation.
Replace m with 124!
We get 125*(124!) , 25*(124!) , 5*(124!).
Note the ratio remains the same and 125 retains its character so do the others. Q.E.D.
Mally

[Wacky]

Originally Posted by mfgoode

To reiterate, we started with the terms, 125 ,25 ,5.
Then we extended it to 125m , 25m , 5m where m denotes an integer/operation.

Yes, this is the same as "125 X" that I mentioned earlier.

Replace m with 124!
We get 125*(124!) , 25*(124!) , 5*(124!).

But your first term is not the same thing as 125!. It is only arithmetically equal to it.

Further, I protest that "125*(124!)" is an expression with six digits in it. Therefore it is not "a three digit number"

It's one thing to stretch the rules of a puzzle. However, IMHO, you have totally broken them with this claimed answer.

[mfgoode]

Originally Posted by Wacky

Yes, this is the same as "125 X" that I mentioned earlier.

But your first term is not the same thing as 125!. It is only arithmetically equal to it.

Further, I protest that "125*(124!)" is an expression with six digits in it. Therefore it is not "a three digit number"

It's one thing to stretch the rules of a puzzle. However, IMHO, you have totally broken them with this claimed answer.

[QUOTE=mfgoode] Be that as it may lets lift the restriction to any finite no. of digits by considering
125m : 25m : 5m.
[Note: BTW 25m is the G.M of 125m and 25m][UNQUOTE]

My dear friend Richard,
125! is arithmetically equivalent in value to 125*(124!). It may not look like 125! but it is.
As a matter of fact there are at least 125 ways of writing 125!
Thus : 125!=125*(124!) =125*124*(123!) = 125*124*123*(122!)=125*124... 3*2*1. These can all be the first term. All this is compressed by writing 125!
mally