Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Finding a Sequence of Numbers

Date: 08/13/2002 at 18:28:28
From: Kirsti
Subject: Algebra

There are six digits in a sequence: two 4's, two 5's, and two 6's.  
There is one digit between the two fours; there are two digits between
the two fives; and there are three digits between the two sixes.  
Write this sequence of numbers.  

My problem is I can't figure the answer to this question; that's why 
I came here.

I have tried many things to figure it out and I have looked in books 
from the library, I have asked my teacher, I have asked my parent's, 
and I have asked my friends. Please help me. 

Thank You!


Date: 08/13/2002 at 21:22:09
From: Doctor Ian
Subject: Re: Algebra

Hi Kirsti,

It's important to attack a problem like this systematically, so that 
you don't end up trying the same answers over and over again, like 
someone wandering lost in the woods. 

The sequence will look like this:

  _ _ _ _ _ _

There is one digit between the two 4's, so that means the following 
are the only possibilities:

  4 _ 4 _ _ _

  _ 4 _ 4 _ _

  _ _ 4 _ 4 _

  _ _ _ 4 _ 4

Now, there are two digits between the two 5's. Let's look at each of 
our possibilities, and see which ones can be extended to take this 
second condition into account. In each case, there is only one 
possibility:

  4 _ 4 _ _ _   =>  4 5 4 _ 5 _

  _ 4 _ 4 _ _   =>  _ 4 5 4 _ 5

  _ _ 4 _ 4 _   =>  5 _ 4 5 4 _

  _ _ _ 4 _ 4   =>  _ 5 _ 4 5 4

In which of these sequences can you insert a pair of 6's that will be 
separated by three digits? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Puzzles
Middle School Puzzles

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/