Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Topic: Clever curiiosity --prove?
Replies: 4   Last Post: Aug 26, 2013 10:19 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Barry Schwarz

Posts: 84
Registered: 3/13/08
Re: Clever curiiosity --prove?
Posted: Aug 26, 2013 4:52 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mon, 26 Aug 2013 12:57:08 -0500, Pfsszxt@aol.com wrote:

> Take ANY three consecutive numbers with the largest divisible by 3.
>Add them.
> If the sum as multiple digits add the digits. Else done.
> Again if multiple digits, add them, etc etc.
> Once you arrive at a single digit number the result will be 6.

There are ten possible sets of numbers {a, b, c} that can be chosen
where the c is 30 or less. It is trivial to show that for these ten
cases, the assertion is true.

For any sequence where the final number exceeds 30, the number are of
the form {k*30+a, k*30+b, k*30+c} where a, b, and c form one of the
previous sets with c <= 30. The sum of these digits is obviously
3*k*30 + a+b+c
which will resolve to k*90 + 6. This can be expressed as
(k-1) * 90 +90 +6 =>
(k-1)*90 + 9 + 6 =>
(k-1)*90 +15 =>
(k-1)*90 + 6
Repeating this process another k-1 times produces a final sum of 6.

> If the three consecutive numbers had the smallest divisible by three,
>the result will always be 3.
>If the middle one , etc, thre result will always be 9.

Each assertion has only 10 distinct cases. Exhaustive computation
seems the easiest way.

Remove del for email

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2015. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.