Kiddie problem.

[Wacky]

Originally Posted by mfgoode

125! is arithmetically equivalent in value to 125*(124!).

Yes, I said so and you quoted that statement in your response.

However, "arithmetically equivalent" is not "the same as".
For two things to be "the same", they must be equivalent in all properties.

You will agree that "100 - 98" is arithmetically equivalent to "2".
However, only one of the expressions is "a single digit number".

In your case, you have claimed that "125!" is a solution because it is "arithmetically equivalent" to the expression "125*(124!)".

Although I argue that the expression "125*(124!)" does not fit other requirements of the puzzle, I will concede that removing the first digit does yield an expression, namely "25*(124!)", which evaluates to 1/5 of the previous expression.

However if you start with the expression "125!", and as stated in the puzzle "you take away the 1st digit" the result is "25!" which does not evaluate to 1/5 of the previous expression.

Thus "125!" is NOT a solution to the puzzle.

[mfgoode]

Originally Posted by Wacky

Yes, I said so and you quoted that statement in your response.

However, "arithmetically equivalent" is not "the same as".
For two things to be "the same", they must be equivalent in all properties.

"Although I argue that the expression "125*(124!)" does not fit other requirements of the puzzle, I will concede that removing the first digit does yield an expression, namely "25*(124!)", which evaluates to 1/5 of the previous expression.

However if you start with the expression "125!", and as stated in the puzzle "you take away the 1st digit" the result is "25!" which does not evaluate to 1/5 of the previous expression.

Thus "125!" is NOT a solution to the puzzle.

To get a better perspective of this entire thread I printed it out fully and was surprised it was 25 pages long.
I have had a long journey, and, of note, I met milestones like William and Cheesehead and you Richard ,amongst others, along the road.
But now Richard we have come to a fork. You have chosen the right path and I the left and so we must part company. This is a controversy that never will be reconciled.

The difference of opinion is in the symbolic notation.
It is not an unusual occurrence. The History of maths is replete with disagreements, sometimes, even bitter. Eg. Isaac Newton versus Gotfried W. Leibniz ; Leopold Kronecker against Georg Cantor to name a few.
The topics they discussed are mountains, compared to the mole hill we are engaged in, which started as a problem for kids from a kiddie newspaper.
Still I am grateful to where it led us.

But now its time to move onto greener pastures. I hope that by going our separate ways we again interact in yet another interesting thread.
Thank you Richard.
Mally