Arrange the integers 1-100 in such a way that no eleven of the numbers selected from left to right form a strictly increasing or decreasing sequence Arrange the integers 1-100 in such a way that no eleven of the numbers selected from left to right (adjacent or otherwise) form a strictly increasing or decreasing sequence.  (This means if 11 numbers are selected from anywhere in the pattern they cannot be in an increasing or decreasing pattern).

I think I have to divide the 100 integers into 10 groups, all with 10 integers.  But that's all I've thought about.
 A: To reiterate my comment from above and remove this from the unanswered queue:
Think about the smaller question of arranging the numbers $1$-$9$ in such a way that there is no monotonic subsequence of length $4$ or more.
$789~456~123$ satisfies this condition.  If you were to create an increasing subsequence all of the numbers must be from the same block.  If you were to create a decreasing subsequence all of the numbers must be from different blocks.  As such, the largest length increasing subsequence is the size of a block and the largest length decreasing subsequence is the number of blocks, both of which in this case are three.
Generalize this to your specific problem.

$91,92,93,\dots,100,~~81,82,83,\dots,90,~~71,72,73,\dots,80,~~\dots~~1,2,\dots,10$

A: What about 
$$10\ 9\ 8\ 7\ 6\ 5\ 4\ 3\ 2\ 1\ 20\ 19\ 18\ 17\ 16\ 15\ 14\ 13\ 12\ 11\cdots $$
?
A: I'd like to point out another construction:
$$91,81,71,\ldots,92,82,72,\ldots,93,83,73,\ldots
$$
If you want an increasing sequence, no matter which number you choose you must pass at each step to the next block of ten numbers $\implies$ at most ten choices.
If you want a decreasing sequence you must lower at each step the ten's figure $\implies$ at most ten choices.
