From: ad@dcs.st-and.ac.uk Subject: Making 59 from 1998 Date: Wed, 17 Dec 1997 06:21:29 -0600 Newsgroups: rec.puzzles,sci.math My son was given one of those puzzles to make certain numbers by combining given digits with the 'usual' operators. Here the digits are 1, 9, 9, 8 and they all have to be used EXACTLY ONCE and IN THE ORDER GIVEN. They can be combined using any number of the operators +, -(negate and/or subtract), *(times), /(divide), ^(power), factorial, square root, nth roots (but this uses the digit n), concatenate(but original digits only - so sqrt(9)8 does NOT make 38), decimal point (again on original digits only), repeater dots . . (e.g. .989 makes 989/999) Floor and ceiling functions are NOT allowed. Matching brackets are allowed Most of the numbers up to 100 are fairly easy and he went a good deal further. But 59 caused him some difficulty for a long time tho' he got it in the end with what I regard as a remarkable solution. I would be interested to see what others can make of it. Tony Davie, Computer Science, St.Andrews University, North Haugh, St.Andrews Scotland, KY16 9SS, Tel: +44 1334 463257, Fax: +44 1334 463278 mailto:adnospam@dcs.st-and.ac.uk http://www.dcs.st-and.ac.uk/~ad/Home.html but remove 'nospam' 'There is magic in the web' - Othello, Act 3, Scene 4 -------------------==== Posted via Deja News ====----------------------- http://www.dejanews.com/ Search, Read, Post to Usenet ============================================================================== From: Denis Denissenko Newsgroups: rec.puzzles,sci.math Subject: Bravo Fred! How 'bout 68 from 1996? Date: Thu, 18 Dec 1997 16:33:29 +0300 Excellent solution, Fred! How about making 68 from 1996? This is the ONLY number left unsolved in 1996 Puzzle (WITHOUT changing order of digits)! See http://forum.swarthmore.edu/ruth/1996.puzzle.html Actually there are also 65 and 67 missing there. I do have solutions for these thou I'm not quite satisfied with them: 65=-1+99*.(6) 67=1+99*.(6) because I consider using periodic fractions to be "bad manners"... Can anybody suggest anything more decent? ============================= Denis Denissenko, M.Sci. Space Research Institute of Russian Academy of Sciences http://hea.iki.rssi.ru/~denis mailto:denis@kisa.iki.rssi.ru IRC: BigDen on dalnet ICQ UIN: 5538455 ============================= ============================================================================== From: fredh@ix.netcom.com (Fred W. Helenius) Newsgroups: rec.puzzles,sci.math Subject: Re: Bravo Fred! How 'bout 68 from 1996? Date: Wed, 17 Dec 1997 21:05:12 GMT Denis Denissenko wrote: >Excellent solution, Fred! >How about making 68 from 1996? Making reluctant use of a repeated decimal: 68 = (.1...)*(sqrt(9)!)! - sqrt(9)! - 6 = (1/9)*720 - 6 - 6. -- Fred W. Helenius ============================================================================== From: Denis Denissenko Newsgroups: rec.puzzles,sci.math Subject: 1996 Puzzle update Date: Thu, 18 Dec 1997 17:07:53 +0300 Just an addition regarding 1996 puzzle: ( http://forum.swarthmore.edu/ruth/1996.puzzle.html ) I have two more missing numbers solved: 65 = 1+((sqrt9)!/sqrt 9)^6 79 = -1+((sqrt9)!)!/(sqrt9+6) 67 is still nonsatisfactory, 68 missing at all. Also I noticed 50 was solved using .6 which is "mauvais ton" as well. Any ideas? ============================= Denis Denissenko, M.Sci. Space Research Institute of Russian Academy of Sciences http://hea.iki.rssi.ru/~denis mailto:denis@kisa.iki.rssi.ru IRC: BigDen on dalnet ICQ UIN: 5538455 ============================= ============================================================================== From: elkies@ramanujan.harvard.edu (Noam Elkies) Newsgroups: rec.puzzles,sci.math Subject: 67 from 1996 (Re: Bravo Fred! How 'bout 68 from 1996?) Date: 18 Dec 1997 16:07:41 GMT In article <34992629.22CD4B0D@hea.iki.rssi.ru>, Denis Denissenko wrote: >[...] see http://forum.swarthmore.edu/ruth/1996.puzzle.html > >Actually there are also 65 and 67 missing there. I do have solutions for >these though I'm not quite satisfied with them: > >65=-1+99*.(6) >67=1+99*.(6) > >because I consider using periodic fractions to be "bad manners"... Can >anybody suggest anything more decent? Here's something more amusing and equally indecent for 67: 67 = .(1) * sqrt( 9! + sqrt(9^6) ) Of course 65 is also 1 + ( sqrt(9) - .(9) )^6 or 1 + ( .(9)+.(9) )^6 or even 1 + sqrt( sqrt(9)+.(9) )^6. Personally I don't care for decimal fractions, repeating or not, in such puzzles, but de disgustibus non est putandum. NDE ============================================================================== Newsgroups: sci.math From: heiner@news.drb.insel.de (Heiner Marxen) Subject: Re: 1996 Puzzle update Date: Sat, 20 Dec 1997 06:38:47 GMT In article <34992E39.2EA9F5E@hea.iki.rssi.ru>, Denis Denissenko wrote: >Just an addition regarding 1996 puzzle: > >( http://forum.swarthmore.edu/ruth/1996.puzzle.html ) > >I have two more missing numbers solved: > >65 = 1+((sqrt9)!/sqrt 9)^6 >79 = -1+((sqrt9)!)!/(sqrt9+6) 79 = -1/9*(9-6!) >67 is still nonsatisfactory, 68 missing at all. Also I noticed 50 was solved >using .6 which is "mauvais ton" as well. Any ideas? 67 = 1+sqrt(sqrt(9)!*(sqrt(9)!+6!)) 50 = -1-sqrt(9)+9*6 For 68 I have also not found a solution (with digits in order). [I've sent my suggestions to the forum, already] -- Heiner Marxen heiner@drb.insel.de