How many integer sets of 15 contain consecutive equal numbers?

[jjmiller37]

Homework Statement

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?

Homework Equations

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.

 

[NateTG]

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.

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

 

[jjmiller37]

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

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?

 

[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.