Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site brl-tgr.ARPA Path: utzoo!linus!philabs!cmcl2!seismo!brl-tgr!gwyn From: gwyn@brl-tgr.ARPA (Doug Gwyn ) Newsgroups: net.puzzle Subject: Re: Derivative of x! and actual interviews Message-ID: <9915@brl-tgr.ARPA> Date: Fri, 12-Apr-85 02:07:24 EST Article-I.D.: brl-tgr.9915 Posted: Fri Apr 12 02:07:24 1985 Date-Received: Mon, 15-Apr-85 03:30:09 EST References: <1337@decwrl.UUCP>, <383@cavell.UUCP> <441@hou2g.UUCP>, <9746@brl-tgr.ARPA> <1587@ukma.UUCP> Organization: Ballistic Research Lab Lines: 52 > > What is the next number in the series > > 2, 3, 5, 7, ... > > > I sure hope that the next number is 11. Primes, right? > (Boy will I feel dumb if this isn't the right answer.) My point was that there IS no "right answer". Any of the following could be the next number in the sequence: 9 The first element obviously reflects some sort of boundary condition (or is a typo) and subsequent ones are just the odd numbers 11 Primes, yes none These are the only four roots that the polynomial (x-2)(x-3)(x-5)(x-7) has any Depending on what fifth-degree polynomial one chooses 8 The starred exercises on p. 197 of a particular textbook 8 This is a list of the non-perfect positive integers 11 Order of finite groups having unique tables (same as the primes argument, but most people would need proof) none Insufficient information any It's just a game and it's now my turn to pick a number ... And who says "..." isn't a number? Appeals to simplicity do not help, since my first answer is simpler in a strict formal sense than the "obvious" one. You see, the more imaginative you are the less inclined you are to settle for the answer that the testers wanted. Perhaps a better test of intelligence would be to see how long a list of distinct answers with justifications you could produce. (Please! Do not clutter the net with extensions to this list!) I am somewhat bitter about this since in a college board physics test I found myself torn between providing the correct answers to questions about relativity (my specialty) or the answers that they obviously wanted. And there have been a few recent cases of high school students challenging SAT questions when the students found better answers than the expected ones. When I was in high school I found myself in demand for competitions and got to be quite good at puzzling out the thinking of the testers -- not the ability the testing was intended to test!