Name: ____________________
Math 211 POW Three
Due: Monday, Nov 10
Calculator Investigation 3.1: The Number 6174
Source: Bennett / Nelson Companion Website
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.
Step
1
2
3
4
5
Maximum Number
8421
7731
6543
8730
8532
Reverse
1248
1377
3456
0378
2358
Difference
7173
6354
3087
8352
6174
QUESTIONS
1. If you begin with any four-digit number whose digits are not all equal, will the above process always
produce 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?
WRITE UP GUIDELINES
 Type your work
 The Oregon Scoring Guide will not be used to assess this POW.
 For each question: Use a table (as illustrated above) to show your test for three different numbers.
Type your work. Recommendation: Use Excel to perform the computation and to record the results.
A
B
C
Cell C2 is programmed with:
1 Number Reverse Difference
=SUM(A2, -B2)
321
123
198
2
 Answer each question carefully
 Assessment: Your work will be assessed based on the quality of your presentation and the quality of
your written responses.
 Further explorations about WHY question 1 works may result in extra credit points.