From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-2.9 required=5.0 tests=BAYES_00,FREEMAIL_FROM, MAILING_LIST_MULTI autolearn=unavailable autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,cee6b97ef93f6732 X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2001-07-22 08:53:22 PST Path: archiver1.google.com!newsfeed.google.com!newsfeed.stanford.edu!newsfeeds.belnet.be!news.belnet.be!cleanfeed.casema.net!leda.casema.net!isdnet!enst!enst.fr!not-for-mail From: AlZimmerma@aol.com Newsgroups: comp.lang.ada Subject: Re: Programming Contest Date: Sun, 22 Jul 2001 11:51:04 EDT Organization: ENST, France Sender: comp.lang.ada-admin@ada.eu.org Message-ID: Reply-To: comp.lang.ada@ada.eu.org NNTP-Posting-Host: marvin.enst.fr Mime-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Trace: avanie.enst.fr 995817154 62564 137.194.161.2 (22 Jul 2001 15:52:34 GMT) X-Complaints-To: usenet@enst.fr NNTP-Posting-Date: Sun, 22 Jul 2001 15:52:34 +0000 (UTC) Cc: comp.lang.ada@ada.eu.org To: maa@liacc.up.pt Return-Path: X-Mailer: AOL 5.0 for Windows sub 138 Errors-To: comp.lang.ada-admin@ada.eu.org X-BeenThere: comp.lang.ada@ada.eu.org X-Mailman-Version: 2.0.4 Precedence: bulk List-Help: List-Post: List-Subscribe: , List-Id: comp.lang.ada mail<->news gateway List-Unsubscribe: , List-Archive: Errors-To: comp.lang.ada-admin@ada.eu.org X-BeenThere: comp.lang.ada@ada.eu.org Xref: archiver1.google.com comp.lang.ada:10419 Date: 2001-07-22T11:51:04-04:00 Mario, Thank you for your interest in the Darts Contest. > ". . . the 5 areas have values (1, 2, 4, 7, 11). Then the smallest > unattainable score is 27." > > I don't get it. If the three darts hit 11, isn't the (attained) score 33? > > And isn't the smallest unattainable score = largest attainable + 1? > > And so wouldn't values (Infinity, ...) be a trivial solution to any N? > > What am I missing? It isn't true that smallest unattainable score is exactly one more than the largest attainable. In the example, you are correct that 33 is the largest attainable score. But there are a few scores smaller than 33 which cannot be attained. And 27 is the smallest of these. To see this, observe that scores from 1 through 26 are demonstrably attainable: 1 = 1 2 = 2 3 = 1 + 2 4 = 2 + 2 5 = 1 + 4 6 = 2 + 4 7 = 7 8 = 1 + 7 9 = 2 + 7 10 = 1 + 2 + 7 11 = 11 12 = 4 + 4 + 4 13 = 2 + 4 + 7 14 = 7 + 7 15 = 4 + 11 16 = 1 + 4 + 11 17 = 2 + 4 + 11 18 = 7 + 11 19 = 4 + 4 + 11 20 = 2 + 7 + 11 21 = 7 + 7 + 7 22 = 11 + 11 23 = 1 + 11 + 11 24 = 2 + 11 + 11 25 = 7 + 7 + 11 26 = 4 + 11 + 11 But there's no way to attain 27. Please let me know if this doesn't answer your question. Al Zimmermann