Read Me - Palindromic Differences Instructions (Word Format) (22.0K)

The Math Investigator is a data collection software program that may be used to collect data for the investigation. You may type answers onto the Word file or copy and paste in data from the Investigator.

Math Investigator 3.2

PALINDROMIC DIFFERENCES on the Math Investigator computes the differences of numbers and their reverses.

In the example shown below, we begin with 723, reverse its digits, and subtract the smaller of the two numbers from the larger. This process of reversing digits and subtracting is continued in steps 2, 3, and 4 until a palindromic number is obtained.

1. Investigate all two-digit numbers to determine: if the process always produces a palindromic number; the maximum number of steps required; and the palindromic numbers obtained by this process.
2. Investigate three-digit numbers. Do they always lead to palindromic numbers and what is the maximum number of steps required?
3. List a few patterns and observations from the data in #1 and #2. Write some conjectures regarding larger numbers and predict whether or not palindromic numbers will be obtained. Describe any patterns you feel may exist in the palindromic numbers obtained by beginning with numbers having more than 3 digits.
4. Test your conjectures from #3. Do they hold? If not, can you find any new patterns?
5. Some four-digit and five-digit numbers that do not lead to palindromic numbers will lead to an unending loop or cycle of numbers. Find some of these numbers. (Hint: Do a systematic search.) What do these numbers have in common?