[seqfan] Re: Simple Puzzler

[Andrew Weimholt]

On Sun, Feb 6, 2011 at 4:51 PM, David Wilson <davidwwilson at comcast.net> wrote:
> Divide your paper into 3 sections. In one section write the number 2, in a different section write the number 3. Thereafter, if two numbers are in distinct sections, write their product in the third section. For example, 6 = 2*3 goes into the initially empty section, then 12 = 2*6 goes into the same section with 3, etc.
>
> 1. Does the same number ever end up in two distinct sections?
>
> 2. Obviously all numbers will be of the form 2^k * 3^j with j,k >= 0. Which of these numbers never appear?
>

1. No
2. j,k cannot both be even

first section has k odd, j even
second section has k even, j odd
third section has j,k both odd

Nice puzzle!

Andrew