From rchapman@mpce.mq.edu.au Sat Mar 13 20:29:19 1999 Received: from macadam.mpce.mq.edu.au (root@[137.111.216.12]) by clinch.math.niu.edu (8.9.1a/8.9.1) with ESMTP id UAA17204 for ; Sat, 13 Mar 1999 20:29:16 -0600 (CST) Received: from landau.mpce.mq.edu.au (landau.mpce.mq.edu.au [137.111.90.60]) by macadam.mpce.mq.edu.au (8.8.8/8.8.8) with ESMTP id NAA07333 for ; Sun, 14 Mar 1999 13:29:13 +1100 (EST) Received: from mpce.mq.edu.au (localhost [127.0.0.1]) by landau.mpce.mq.edu.au (8.9.1/8.9.1) with ESMTP id MAA02784 for ; Sun, 14 Mar 1999 12:29:11 +1000 (EST) Sender: rchapman@mpce.mq.edu.au Message-ID: <36EB1EF7.3C4CA217@mpce.mq.edu.au> Date: Sun, 14 Mar 1999 12:29:11 +1000 From: Robin Chapman X-Mailer: Mozilla 4.05 [en] (X11; I; OSF1 V4.0 alpha) MIME-Version: 1.0 Newsgroups: sci.math To: Dave Rusin Subject: Re: How to recognize Mathematician in a crowd References: <7bnr9r$je5$1@uwm.edu> <36E527CA.176E7726@computer.org> <7c3eln$5p1$1@gannett.math.niu.edu> <36E5956B.1A2812DA@mpce.mq.edu.au> <7cbch4$7bh$1@gannett.math.niu.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Content-Transfer-Encoding: 7bit Status: R Dave Rusin wrote: > > I appreciate the several posts introducing Vorderman; now I'm ready for idle > chit-chat with visiting Brits. I must say that Chapman's comment > > She is indeed a highly qualified and talented person, having a degree from > > the University of Cambridge (third-class in Engineering I believe). > makes me wonder now, not about her qualifications to be a Smart Person > but rather about her qualifications to be a Television Personality; > at least, my exposure to the American species of TP led me to expell > the idiot box from my home. > > Robin Chapman further wrote: > >She is a TV personality. Since 1982 she has appeared on the quiz show > >_Countdown_ shown on Channel 4. Her speciality is the _Nubers Game_. Carol > >turns over 6 cards each revealing a number. She then presses a button > >causing a computer to generate a three-digit random number. The contestants > >then attempt to form this number by using the six numbers on the cards and > >the four basic arithmetic operations. Should they fail to do so, the lovely > >Carol then shows how it's done, demonstrating that she has brains as well > >as beauty. > > How, exactly, is it done? We are given six numbers (integers? digits?) a_i > and a target integer N in [100, 999]; we are asked to find a sequence op_j > of length five from {'+', '-', '*', '/'} and a balanced arrangement of > parentheses so as to have a1 op1 a2 op2 ... a5 op5 a6 = N (suitably > grouped on the left) -- is that the game? I have played other variants of > this game with just four a_i, and saw no real method of attack for the > general problem other than an exhaustive search. Some reduction of the > search space can be accomplished using the commutative laws and so on, > but this is still a daunting task. A human can often beat a machine, but > some examples are trickier (and indeed, some admit no solution, a result > which I think is hard to establish without complete enumeration). > > Also unclear: are fractional nintermediate results allowed? (Example: > combine {a_i} = {3, 3, 7, 7} to make N=24.) > > My take on the (4+1)-number variant is summarized at > http://www.math.niu.edu/~rusin/papers/uses-math/games/krypto/index.html > A more precise description of the numbers game. Carol has 24 cards face down with the numbers 1 to 10 twice and the numbers 25, 50, 75 and 100. These big numbers are in a separate row. One of the contestants asks Carol for k big numbers and 6-k small numbers where 0 <= k <= 4. The usual practice is to go for 1 large and 5 small (this means that it's usally easy to solve). Then she press the random number machine. This comes up with a 3-digit number. I suspect this means never < 100 and I also suspect that "round" numbers such as multiples of 100 are barred too. The contestants have to make the desgnated number using the numbers on the cards no more than once (they don't have to use every number). When dividing one has to have a positive integer quotient. The contestant nearest the designated number wins (as long as it's within 10) and scores according to how close they get. But htis isn't all that's in the show. There's also the "letters game" and the "Countdown conundrum". Exciting stuff! -- Robin Chapman + "Going to the chemist in Department of Mathematics, DICS - Australia can be more Macquarie University + exciting than going to NSW 2109, Australia - a nightclub in Wales." rchapman@mpce.mq.edu.au + Howard Jacobson, http://www.maths.ex.ac.uk/~rjc/rjc.html - In the Land of Oz From rusin@math.niu.edu Mon Mar 15 08:38:28 1999 Received: from vesuvius.math.niu.edu (vesuvius.math.niu.edu [131.156.3.93]) by clinch.math.niu.edu (8.9.1a/8.9.1) with ESMTP id IAA21462; Mon, 15 Mar 1999 08:38:28 -0600 (CST) From: Dave Rusin Received: (from rusin@localhost) by vesuvius.math.niu.edu (8.8.8/8.8.5) id IAA02223; Mon, 15 Mar 1999 08:38:27 -0600 (CST) Date: Mon, 15 Mar 1999 08:38:27 -0600 (CST) Message-Id: <199903151438.IAA02223@vesuvius.math.niu.edu> To: rchapman@mpce.mq.edu.au Subject: Re: How to recognize Mathematician in a crowd Cc: rusin@math.niu.edu Status: R OK, thanks for the clarification of the numbers game. It still must happen from time to time that even the game host is stumped? I mean, not all these problems are solvable, and even the ones that are, are not always evident. For example, the task "combine 1, 5, 8, 14, 19 to make 13" has a unique solution according to the rules in the variant I play (all cards must be used) and I'm sure such examples occur with the other variants too. By the way, you're right: I really must get my own copy of Graham et al. There are quite a few must-buy's on my list waiting until my children have finished college -- seven years from now :-( dave