Zingers

Date: 11/06/2002 at 13:25:10
From: Kathi Stanley
Subject: Numbers - Zingers

The question is from an extra credit family brain teaser for my 5th 
grader:

The following numbers are zingers: 

   9,41,57,73,17,89,33

The following numbers are not zingers: 

   7,22,45,8,59,36,68,13

Which of the numbers below are zingers?

   4,55,63,25,49,24,77,92,38,42,20,65

We've tried to come up with a pattern, but just can't figure it out.  
We'd all greatly appreciate any help you can provide. Thanks so much!

Date: 11/06/2002 at 14:12:22
From: Doctor Greenie
Subject: Re: Numbers - Zingers

Hello, Kathi -

"Zinger" is not part of standard mathematical terminology, but 
sometimes a teacher will make up a term like 'zinger' in the course of
a lesson about identifying patterns.

It should help if you put the given list of zingers in numerical 
order:

  9, 17, 33, 41, 57, 73, 89

These numbers by themselves probably don't suggest a pattern or a 
common trait for zingers. But let's look at the differences between 
the zingers we have:

   9  17  33  41  57  73  89
     8  16   8  16  16  16

The differences between the zingers we have are all multiples of 8; 
this means that the difference between any two zingers is a multiple 
of 8. Because the difference between any two zingers is a multiple 
of 8, the common trait that zingers have is that they all leave the 
same remainder when divided by 8.

So now you can examine the other candidates to see which numbers are 
zingers and which are not.

I hope this helps. Please write back if you have any further 
questions about this.

- Doctor Greenie, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 11/06/2002 at 15:32:22
From: Kathi Stanley
Subject: Thank you (Numbers - Zingers)

Wow!  Thank you very much!