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Math Investigation
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The Investigation poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find.

Click on the Read Me file below to open the investigation in a Word file:

Read Me - The Number 6174 Instructions (Word Format) (30.0K)



Calculator Investigation 3.1

The Number 6174

There is something very special about the number 6174. Select any four-digit number whose digits are not equal, and arrange the digits to form the largest possible number, that is, put the digits in decreasing order from left to right. Then form the reverse of this number and subtract it from the larger number. Continue this process by forming the largest possible number from the difference and subtracting the reverse. The example in the following table shows the process ending with 6147 after five steps.

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072532947/78543/CI_3_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (20.0K)</a>Starting Points for Investigations
  1. If you begin with any four-diit number whose digits are not all equal, will the above process always product 6174?
  2. What happens when this process is applied to three-digit numbers whose digits are not all equal? Is there a special number in this case?
  3. What happens when the process is applied to five-digit numbers? Is there a special number in this case?
  4. You may wish to continue this investigation for numbers with more digits.





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