Find -the- soultion
 

I was given this puzzle today (the person that gave it to me got it from another source). I was able to solve it quite quickly. An engineer with years of experience was unable to get the answer, even with a big clue. Once I hand lead them through it, they finally go the answer.

As usual, [B][FONT="Arial Black"][COLOR="Red"]spoilerize[/COLOR][/FONT][/B] your answers and if you are a genius and get it very quickly wait for others a bit before posting the answer. For those that don't get it and don't want to look at the spoilerized answers, I will post a clue after a bit. :yzzyx:


Given the sequence below, please solve the equation or reduce it to the simplest form possible.
(x + a) (x - b) (x + c) (x - d) ...continuing to... (x - z) = ?

Found it!

I posted a similar polynomial here in Puzzles about eight years ago -

[spoiler]
(x-x) is one of the factors
[/spoiler]

(The old thread was locked.)

[QUOTE=davar55;391663]I posted a similar polynomial here in Puzzles about eight years ago[/QUOTE]The original source that was cited is at least a year old. The root source could be the same.

[QUOTE=Uncwilly;391665]The original source that was cited is at least a year old. The root source could be the same.[/QUOTE]

Maybe the VERY VERY root source, since I remember this from HS math team, circa 1972.

[spoiler]A potential solution relies upon the reader seeing a pattern and then assuming that the pattern continues without interruption. But I see nowhere that such an assertion can be made with 100% certainty. The only possible saving grace for this is the assumption that the answer must be some very simple form else it is really just a headache creating source of algebraic torture. And of course we all know the next number in the sequence (1,2,3,...) can be any number one chooses it to be, so perhaps we should make the same conclusion for (a,b,c,d,z). Note that the phrase "continuing to" does not necessarily mean there are intervening terms, it could simply mean the following term is the next in the sequence.[/spoiler]

[/puzzle pedantism]

The similar puzzle I referred to is in thread "Algebra Problem" from April 2006 P.B.

That is a very old problem, one of our teachers in middle school told it to us [edit: about 40 years ago]. I was the best :razz: in my class at math at that time, in a small provincial town (about 20k people), but no, I did not get the solution immediately, but only after some playing with the numbers for a while, hehe. The simplest form you can write this polynomial is [SPOILER] 0 (i.e. zero, because in the string you have x-x somewhere) [/SPOILER]

[QUOTE=Uncwilly;391656]I was given this puzzle today (the person that gave it to me got it from another source). I was able to solve it quite quickly. An engineer with years of experience was unable to get the answer, even with a big clue. Once I hand lead them through it, they finally go the answer.

As usual, [B][FONT="Arial Black"][COLOR="Red"]spoilerize[/COLOR][/FONT][/B] your answers and if you are a genius and get it very quickly wait for others a bit before posting the answer. For those that don't get it and don't want to look at the spoilerized answers, I will post a clue after a bit. :yzzyx:


Given the sequence below, please solve the equation or reduce it to the simplest form possible.
(x + a) (x - b) (x + c) (x - d) ...continuing to... (x - z) = ?[/QUOTE]

I see an expression. I see no equation. This problem is poorly posed.

Furthermore, the sequence of +/- operators that appear in the individual terms is not well
defined. One could easily define a sequence in which (x+x), rather than (x-x) appears.
For example: all terms use + except for those whose alphabetic index (a=1, b=2, ...) are either a
positive power of two or twice an odd prime. etc.

[QUOTE=R.D. Silverman;391721]I see an expression. I see no equation. This problem is poorly posed[/QUOTE]
Bob, this was posted in the Puzzles forum, not the Math forum. Please understand that by their nature, puzzles require assumptions to be made. Borrowing and adapting from another source:
"All puzzles appearing in the Puzzle forum have been painstakingly researched, although the answers have not. Ambiguous, misleading, or poorly worded puzzles are par for the course. Readers who are sticklers for the truth should post their own questions in the math forum."

[QUOTE=Uncwilly;391723]Bob, this was posted in the Puzzles forum, not the Math forum. Please understand that by their nature, puzzles require assumptions to be made. Borrowing and adapting from another source:
"All puzzles appearing in the Puzzle forum have been painstakingly researched, although the answers have not. Ambiguous, misleading, or poorly worded puzzles are par for the course. Readers who are sticklers for the truth should post their own questions in the math forum."[/QUOTE]

I thought the puzzle was perfectly clear. Let he who is w/o puzzle cast the first criticism.