Being a mathematician, I will define a digit function where the function of
a 3-digit number is defined as follows.
1. Add the digits. If the sum is a single digit, that digit is the output.
2. If the sum is 2 digits, add the digits again and that digit is the
output.
For example f(769) = 4 because 7 + 6 + 9 = 22 and 2 + 2 = 4.
The interesting number theory connection is that if you take the 3 digits
and form any combination of a 2 digit number and a 1 digit number and add
the numbers, then add the digits (more than once if necessary), the final
output digit will be the same.
For example, take the digits 7, 6, and 9 to form 79 + 6 = 85. 8 + 5 = 13, 1
+ 3 = 4, giving f(769).
Likewise, 96 + 7 = 103, 1 + 0 + 3 = 4 which is also f(769).
I have experimented with several 3-digit numbers and in all cases, the sum
of any 2-digit number and the remaining digit map (as indicated above) to
f(number) as defined above.
I have also experimented with 4-digit numbers and various combinations of 3
and 1-digit numbers added and mapped, then 2-digit and 2-digit numbers from
the 4-digits mapped to the sum of the 4-digits mapped to a single digit as
above. In every case, I find that the mappings all lead to the same single
digit. Does anyone know of such a pattern that has been studied in number
theory? Is there a proof that such a phenomenon holds for n-digit numbers?
By the way, on grading, in Basic Math this semester, my students are getting
a 0 grade for any quiz/test less than 80%. Before they can take a retake,
they must get the signature from a tutor in the math lab that they have gone
through the test and worked more problems like the ones they missed. So
far, students have grumbled a bit, but have gotten help. I have required
retakes before, but this is the first time I have required students to get
help from someone besides me before taking a retake. This is making a big
difference in the time I spend on the class.
Martha
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************