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

2)How many arrangements of the integers 1,2,3,...,n are there such that each integer differs by one (except for the first integer) from some integer to the left of it?

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.

## Answer This Question

## Related Questions

- PROGRAMMING - 1. Make a C program that will input two integers and then to enter...
- Algebra - A.Write and solve an equation to find three consecutive integers with ...
- Algebra - A.Write and solve an equation to find three consecutive integers with ...
- Math - One integer is 4 more than a second integer. Three times the first ...
- algebra - Find the two consecutive odd integers such that 5 times the first ...
- Math - Find three consecutive even integers such that the sum of the smallest ...
- Algebra - Find two consecutive odd integers such that 5 times the first integer ...
- math - there are 8 consecutive integers that add up to 31. Only two of the ...
- math - Find two consecutive integers such that the sum of 3 times the first ...
- la sallle - There are 3 consecutive even integers such that the quotient ...

More Related Questions