Wednesday

April 16, 2014

April 16, 2014

Posted by **Laura** on Sunday, October 15, 2006 at 10:41am.

Let's construct the arrangement.

First consider 1, it can only have two placed next to it so it has to be at the end or beginning. Do you see why?

Ok, so let's suppose the arrangement starts with 1, then the only number that can come after it is 2, then 3 then 4...

Now suppose 1 is at the end. Then the only number that can come before is 2, then 3 then 4...

The only two arrangements are

1 2 3 4 5 ... n-1 n and

n (n-1) (n-2) ... 3 2 1

By the way, we are not constructing a digit, but rather an arrangement for the first n integers.

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