How many integer sets of 15 contain consecutive equal numbers?

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Homework Help Overview

The problem involves determining the number of integer sets of 15 from the integers 1 to 500, specifically focusing on whether any of these sets contain consecutive equal numbers. There is some ambiguity regarding the definition of an "integer set of 15" and the concept of "consecutive numbers being equal."

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express confusion about the terminology used in the problem statement, particularly regarding what constitutes an integer set of 15 and the meaning of consecutive equal numbers. Some participants attempt to rephrase the question for clarity, while others suggest that the original wording may be problematic.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the problem's wording. Some have proposed rewording the question to focus on integer sequences of multiples of 15, while others are exploring the implications of selecting numbers and the potential for consecutive equal numbers.

Contextual Notes

There is a lack of clarity in the problem statement, which has led to multiple interpretations and suggestions for rephrasing. The constraints of the problem, such as the range of integers and the specific conditions for the sets, are under discussion but not fully resolved.

jjmiller37
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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.
 
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jjmiller37 said:
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.
 
NateTG said:
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?
 
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.
 

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