[superprismatic]

The words of a problem are numbered in lexicographical

order. Then the first word of the problem is written

in the position denoted by 1, the second word in the

position denoted by 2, etc. The result is: "five

random order is eight that numbers six one square four

are the what a written digit is resulting number

probability and three in down the the." Solve the

(mathematical) problem.

SUPERPRISMATIC'S ATTEMPT AT CLARIFICATION:

Suppose the original (mathematical) problem

were "two plus three add to what number?"

first we label each of the 7 word positions

1,2,3, etc. in alphabetical order. Since

"add" is first alphabetically, we label it 1,

since "number" is second alphabetically, we

label it 2, etc. Writing the sentence above

the labels, we get

"two plus three add to what number"

6 3 4 1 5 7 2

So, we place the first word ("two") into

the position labelled 1, the second word

("plus") into the position labelled 2, etc.

Thus, our result is

6 3 4 1 5 7 2

"what three add two to number plus".

So, had the puzzle had this result instead

of "five random order is eight....", the

answer to the (mathematical) problem would

have been 5.

[Guest]

What is the probability that the numbers one, three, four, six, eight are written down in random order and the resulting five digit number is a square

[superprismatic]

What is the probability that the numbers one, three, four, six, eight are written down in random order and the resulting five digit number is a square

This can't be the problem because the statement in the problem would have ended "what the" instead of "the the" which it is.

[Guest]

ive tried to work it out and what Ive got so far

i dont think the puzzle starts with "what" based on you have to make a choice based on "the" and neither work. im guess "are" first, "is" second, and last choice is "in". Not sure tho.

[Guest]

gadaju was on the right track.

The numbers one, three, four, six, and eight are written down in random order. What is the probability that the resulting five-digit number is a square?

[Guest]

Therefore...

There are (I believe) 5 numbers that fit those criteria: 16384 = 128², 31684 = 178², 36481 = 191², 38416 = 196², and 43681 = 209². And there are 120 ways to arrange five numbers randomly (5 x 4 x 3 x 2 x 1 = 120). So, the probability would be 5/120 = 1/24 = 4¹/₆%

Edited July 31, 2009 by nuclearlemons

[Guest]

gadaju was on the right track.

The numbers one, three, four, six, and eight are written down in random order. What is the probability that the resulting five-digit number is a square?

Thanks NL:

As a linguist, I figured that we could just try to make a syntax-valid sentence using the given parts of speech. In a few minutes, I came up my sentence, which you'll notice is semantically identical (in terms of what is given and what is being asked) to the original, un-encoded question. What I thought was interesting was that I could answer question 2 regardless of how the words in the question 1 were jumbled. In fact, i put the words in alphabetical order to "solve" question 1 using regular old inference and syntax rules.

Did you decode the message using a process?