# Consecutive number problem

1. Jan 31, 2008

### jjmiller37

1. The problem statement, all variables and given/known data
Given the integers from 1 to 500. How many integer sets of 15 are there?
Do any of the integer sets contain consecutive numbers that are equal?

2. Relevant equations

3. The attempt at a solution

I do not know what is meant by an integer set of 15.
I do not know what is meant by consecutive numbers being equal.

2. Jan 31, 2008

### NateTG

You're not the only one. If the problem is really written that way (in English) hand it to the teacher, and complain.

3. Jan 31, 2008

### jjmiller37

Let me try the question again. I asked for a rewording of the question and here it is:
Consider all of the integer sequences of value n>0 where each number is a multiple of 15 between 1 and 100. How many of these subsets contain consecutive numbers that are equal?

4. Jan 31, 2008

### Dick

That's still a little obscure, but I'll take a guess. There are 6 multiples of 15 in the range. You want to pick a sequence of n of them. There are 6^n ways to do that. Am I ok so far? Now you want to know how many contain consecutive equal numbers? Ask yourself how many don't. Pick the first number, you have six choices. Pick the second number. Now how many choices? Etc.