May 2006 - mathfun@mailman.xmission.com

Re: [math-fun] California Math Exit Exam
by dasimov＠earthlink.net 16 May '06

16 May '06

Don't people know that "tub" means a largish pail, not just a bathtub? --Dan

1 0

RE: [math-fun] California Math Exit Exam
by Russ Cox 16 May '06

16 May '06

> Tina is filling a 45 gallon tub at a rate of 1.5 gallons of water per minute. At this rate, how long will it take to fill the tub? > > A 30.0 minutes > B 43.5 minutes > C 46.5 minutes > D 67.5 minutes > > [What's a "tub" ? Is that like a bathtub? ] 45 gallons would be a very small bathtub. Russ

2 1

RE: [math-fun] California Math Exit Exam
by Cordwell, William R 15 May '06

15 May '06

However, a student who knew only 32 out of 80 questions could guess randomly on the remaining 48 questions, and expect to come very close to the required 44 correct answers; so a student with knowledge at only the 40% level (whatever that means) might expect to pass, as long as there is no penalty for incorrect answers. -----Original Message----- From: math-fun-bounces+cordwell=sandia.gov(a)mailman.xmission.com [mailto:math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com]On Behalf Of Henry Baker Sent: Monday, May 15, 2006 3:07 PM To: math-fun Subject: Re: [math-fun] California Math Exit Exam I didn't really set up this posting correctly. In California, we now (are supposed to) have an "exit exam" for high school students which sets standards for graduation. http://www.cde.ca.gov/ta/tg/hs/ The math portion of the test is approx. 80 questions, each of which is multiple choice with 4 choices. A radio talk show host here in Los Angeles was carrying on about how easy it should be to pass this examination, since it required only a 55% score to pass. If I've done _my_ math correctly, a completely random answer sheet with 20 questions would pass with a probability of ~ 1/254; with 40 questions would pass with a probability of ~ 1/20560, with 60 questions would pass with a probability of ~ 1/1467711, and with 80 questions would pass with a probability of ~ 10^-8. So, our random student would have to take the test on the order of 10 million times to have a good probability of passing it. So monkeys with typewriters probably aren't going to pass. At 08:42 PM 5/14/2006, Henry Baker wrote: >Here's another question to add to the California Exit Exam for >high school students in mathematics: > >If there are 80 questions on this test, and each of the 80 questions >has 4 choices, what is the probability that someone could pass >(>= 55%) [oops, first answer the question of how many questions out >of a total of 80 questions 55% is] the test, if for each question >he chose one of the 4 answers at random (p=25% for each answer). > >Alternatively, assuming that the test preparers aren't insane, >what is the probability that someone could pass the test by always >choosing the "A" answer for each question? > >Extra credit: using this probability, estimate the number of times >one should take the test to raise the probability of passing it at >least once to 80%. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

1 0

[math-fun] eta as theta
by R. William Gosper 12 May '06

12 May '06

oo pi 1/6 /===\ Theta (--, q ) 1/24 | | k 2 6 eta(q) := q | | (1 - q ) = ---------------- . | | sqrt(3) k = 1 This can't be new. Why isn't it more prevalent? Instead I've been using a bletcherous Thetaprime_1(0,sqrt(q)) for (q;q)_oo in the q-Gamma/q-factorial reflection (and q-sin) formulae. --rwg

1 1

[math-fun] Problem Puzzler 1999
by Christian Boyer 10 May '06

10 May '06

Jean-Paul Delahaye publishes in the new issue of Pour La Science a very interesting article on Sudokus. He asked a very strange Sudoku problem WITHOUT any given numbers, only ">" and "<" signs between cells. He mentions that this problem was published in Puzzler, 1999, and that he does not know the solution. I have the solution, sent this morning to J.-P. Delahaye. Now looking for "Puzzler 1999" on Google, I find that Ed Pegg Jr. wrote an article in September 2005 including the same astonishing puzzle, figure 7 "Greater Than Sudoku" in: http://www.maa.org/editorial/mathgames/mathgames_09_05_05.html Perhaps that somebody else had already the solution? Ed, did you receive a solution to your article? Christian.

3 8

[math-fun] Super-fractals: kind of generalization
by Eric Angelini 10 May '06

10 May '06

Hello Math-Fun and SeqFan, ... for those interested, please see «Note of May 10th», at the bottom of the page: http://www.cetteadressecomportecinquantesignes.com/Decimation.htm Best, É.

1 0

[math-fun] Reverse then Add (RADD) sequences
by N. J. A. Sloane 08 May '06

08 May '06

Dear Math Fun: A correspondent from Belgium, Luc Stevens suggested looking at the sequences that I now call RADD sequences (not to be confused with the old RATS, Reverse, Add Then Sort sequences): T(S,Q) is formed by starting with S; to get later terms, reverse previous term annd add Q. (Of course leading zeros are omitted.) For a summary of these sequences, see my article "Sequences of RADD type" that is linked to A117831. This gives a lot of data, including many references to new entries in the OEIS. Example: T(1,1) is 1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,... (A117230) which reaches a cycle of length 9 in 1 step. But T(1,10) never cycles (A117841). My question is, has anyone seen any previous work on these sequences? How can they possibly be new? Surely someone must have determined which ones cycle and which do not? Can anyone supply references? Neil

1 0

[math-fun] Adam Polito Kleber
by Michael Kleber 07 May '06

07 May '06

Jessica Polito, Michael Kleber, and Daniel Polito Kleber are delighted to announce the arrival of Adam Polito Kleber Friday, 5 May, 10:24 p.m., 8 lbs. 9 oz. Mother, father, and big brother are all happily resting at home. Visitors (healthy ones) are generally welcome, but please call first.

1 0

Re: [math-fun] quantifier depth
by Henry Baker 07 May '06

07 May '06

Are you interested in quantifier depth as an indicator of difficulty? I seem to recall that many of the decision procedures get an exponential in quantifier depth. But keep in mind that Hilbert's Tenth Problem has only existential quantifiers, although they are quantifiers over the integers, and this problem is undecidable. At 01:00 PM 5/6/2006, Schroeppel, Richard wrote: >What's the maximum quantifier depth for doing everyday mathematics? > >I count groups of quantifiers of the same type as 1, so that a block >of variables of the shape (all x,y,z), or the statement that there's >a magic square of size 3x3 (exists a,b,c,d,e,f,g,h,i) are counted >as one quantifier. So I'm really talking about Alternating Quantifier >Depth. > >The definition of "a function f is continuous at a point x" has depth 3: > > (all epsilon) (exists delta) (all y) > 0 < |y-x| < delta => |f(y)-f(x)| < epsilon > >and "f is continuous" is also depth 3: > > (all x,epsilon) (exists delta) (all y) etc. etc. > >The theorem that "the sum of continuous functions is continuous" >is depth 5: > > (all f,g) (exists h) (all x,epsilon) (exists delta) (all y) > h(x) = f(x)+g(x) And { 0 < |y-x| < delta => ... } > >So it looks like routine math might use a maximum depth of 8 or so. >Presumably there are a few specialties that go much deeper. (?) >Evaluating a game tree is an example. > >Rich

1 0

[math-fun] Solvable sudoku?
by Bernie Cosell 07 May '06

07 May '06

I was wondering: how does one determine: 1) if a particular sudoku grid is solvable at all, and 2) if a particular sudoku grid is solvable solely by "logic". I realize that there's some disagreement as to which procedures are allowed in "logic only" solutions, but still: is there some way, short of brute-force solving [either with full guess/retrace (1 above) or only using some set of deduction-rules (2 above)] for figuring out if a grid is solvable? /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

3 2