# [seqfan] Re: Simple Puzzler

David Wilson davidwwilson at comcast.net
Mon Feb 7 13:32:48 CET 2011

```Right on 1.

Not quite complete on 2. Nontrivial odd powers of 2 and 3 are also excluded.

----- Original Message -----
From: "Andrew Weimholt" <andrew.weimholt at gmail.com>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Sent: Monday, February 07, 2011 2:36 AM
Subject: [seqfan] Re: Simple Puzzler

> 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

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