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my friend gave me the puzzle and she told me the supposed answer. I am
totally baffled and so are all my friends. so I turn to the freeshell
community for help:
Which number would come next?
4 5 3 4 4 4 3 3 5 7 2 2 4 3
i have tried EVERYTHING.

This is one of those stupid pattern puzzles. It will take time. There HAS
to be a pattern to this. I saw alot of these in one of those IQ tests and
some of them were tricky. I think this does take the cake.

You can devise an equation such that the next number in any sequence is
*anything you want*, like Pi or -215888, which is why I'm not especially
fond of these "find the pattern" puzzles. After all, the "simplest"
pattern (which is usually what's wanted in this type of puzzle) is a matter
of interpretation.
That being said, after a quick glance at the sequence, I have no idea what
the "simplest" pattern might be. The number of letters in some sequence of
words? The first or last digit in some numerical sequence?
4 5 3 4 4 4 3 3 5 7 2 2 4 3
"Egad!" cried the math whiz. "This fun and witty problem is so hard I'll
make up my own answer.
Based on the above paragraph, the next numbers would be 4 2 2 3 6. :-)

first of all, let me say I came up with two potential solutions:
solution 1: 3, since the first and second triplets add to 12, the third
and fourth triplets add to 11. if the pattern continues, then the last
number must be three so as to make the next triplet sum to 10
solution 2: any number, since if you make a 3x5 matrix out of the numbers
(with a _ ) for the missing number, any number substituted for _ will
result in the sum of sums of rows equalling the sum of sums of columns
(kind of like a longitudinal reduncancy check)
BUT THE REAL ANSWER IS that the person who gave my friend the problem
forgot to include all of the information. there was a sentence that
preceeded the phrase (Which number comes next in the series?). The length
of each word in that phrase was what each of those numbers were. So the
length of the fiftheenth word in the phrase would have been the correct
answer.
Sorry to dissapoint you all but I personally enjoyed the mental challenge
of beating my head against an intractable problem.
-Mike