novaBBS - rec.puzzles - Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...

(expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...

<3ba50b09-48b1-4a60-954c-caed5762b540n@googlegroups.com>

https://www.novabbs.com/interests/article-flat.php?id=228&group=rec.puzzles#228

X-Received: by 2002:a05:600c:210a:b0:3a0:3be1:fb8b with SMTP id u10-20020a05600c210a00b003a03be1fb8bmr788354wml.195.1656467298931;
Tue, 28 Jun 2022 18:48:18 -0700 (PDT)
X-Received: by 2002:a05:620a:404d:b0:6a7:d3d:df9b with SMTP id
i13-20020a05620a404d00b006a70d3ddf9bmr531216qko.530.1656467295317; Tue, 28
Jun 2022 18:48:15 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.128.87.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: rec.puzzles
Date: Tue, 28 Jun 2022 18:48:14 -0700 (PDT)
Injection-Info: google-groups.googlegroups.com; posting-host=2601:648:8600:9780:0:0:0:277e;
posting-account=YjTkGAoAAAA4_fbAISfvtIqrYbghMeBx
NNTP-Posting-Host: 2601:648:8600:9780:0:0:0:277e
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <3ba50b09-48b1-4a60-954c-caed5762b540n@googlegroups.com>
Subject: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...
From: henha...@gmail.com (henh...@gmail.com)
Injection-Date: Wed, 29 Jun 2022 01:48:18 +0000
Content-Type: text/plain; charset="UTF-8"

by: henh...@gmail.com - Wed, 29 Jun 2022 01:48 UTC

Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

______________________

Can an ave. 14 y.o. understand (suss out) or figure out using pen and paper that ...

1. these numbers fall between 2 and 3 -------- or between 1 and 9 ?

2. these numbers are converging ... ?

(expt 1.1 10) ---> 2.593742460100002

(expt 1.01 100) ---> 2.704813829421529

(expt 1.001 1000) ---> 2.7169239322355203

(expt 1.0001 10000) ---> 2.718145926824356

(expt 1.00001 100000) ---> 2.7182682371975284

Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...

<t9h4ij$1ktb$1@macpro.inf.ed.ac.uk>

copy mid

https://www.novabbs.com/interests/article-flat.php?id=231&group=rec.puzzles#231

copy link Newsgroups: rec.puzzles

Path: i2pn2.org!i2pn.org!aioe.org!nntp.terraraq.uk!nntp-feed.chiark.greenend.org.uk!ewrotcd!usenet.inf.ed.ac.uk!.POSTED!not-for-mail
From: rich...@cogsci.ed.ac.uk (Richard Tobin)
Newsgroups: rec.puzzles
Subject: Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...
Date: Wed, 29 Jun 2022 09:04:19 +0000 (UTC)
Organization: Language Technology Group, University of Edinburgh
Lines: 9
Message-ID: <t9h4ij$1ktb$1@macpro.inf.ed.ac.uk>
References: <3ba50b09-48b1-4a60-954c-caed5762b540n@googlegroups.com>
NNTP-Posting-Host: macaroni.inf.ed.ac.uk
X-Trace: macpro.inf.ed.ac.uk 1656493459 54187 129.215.197.42 (29 Jun 2022 09:04:19 GMT)
X-Complaints-To: usenet@macpro.inf.ed.ac.uk
NNTP-Posting-Date: Wed, 29 Jun 2022 09:04:19 +0000 (UTC)
X-Newsreader: trn 4.0-test76 (Apr 2, 2001)
Originator: richard@cogsci.ed.ac.uk (Richard Tobin)

by: Richard Tobin - Wed, 29 Jun 2022 09:04 UTC

In article <3ba50b09-48b1-4a60-954c-caed5762b540n@googlegroups.com>,
henh...@gmail.com <henhanna@gmail.com> wrote:

>(expt 1.00001 100000) ---> 2.7182682371975284

This is unsurprising if you consider the binomial expansion of
(1-1/n)^n.

-- Richard

Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...

<t9j5u3$3m2$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/interests/article-flat.php?id=237&group=rec.puzzles#237

copy link Newsgroups: rec.puzzles

Path: i2pn2.org!i2pn.org!aioe.org!SABVAYcHOklaNK/u1FQzwA.user.46.165.242.75.POSTED!not-for-mail
From: emurph...@zoho.com (Edward Murphy)
Newsgroups: rec.puzzles
Subject: Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...
Date: Wed, 29 Jun 2022 20:39:47 -0700
Organization: Aioe.org NNTP Server
Message-ID: <t9j5u3$3m2$1@gioia.aioe.org>
References: <3ba50b09-48b1-4a60-954c-caed5762b540n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="3778"; posting-host="SABVAYcHOklaNK/u1FQzwA.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.10.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Edward Murphy - Thu, 30 Jun 2022 03:39 UTC

On 6/28/2022 6:48 PM, henh...@gmail.com wrote:

> Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

[spoiler space]

I think you can place #1 horizontally, then #2 #3 #4 horizontally on top
of #1 and forming a triangle with its center above #1's center, then #5
vertically so that it touches #1's center as well as the others. (This
depends on them being thin enough compared to their diameters.)

Ontogeny recapitulates phylogeny.

interests / rec.puzzles / Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...

Subject	Author
(expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...	henh...@gmail.com
Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...	Richard Tobin
Re: (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...	Edward Murphy