November 2005 - mathfun@mailman.xmission.com

[math-fun] m * ultipl = ication
by Eric Angelini 22 Nov '05

22 Nov '05

m * ultipl = ication In this multiplication, same letters stand for same digits and different letters stand for different digits : what is the above letter which can also be found in the digit it stands for ? Best, É.

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[math-fun] Re: math-fun Digest, Vol 33, Issue 9
by Phil Carmody 22 Nov '05

22 Nov '05

> Sharpen your No. 2 pencils please, then click the URL below > > http://www.flickr.com/photos/thane/65247884/ Given that Q is less than 8 from the west coast, it must be the distance to P that's wrong. Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed [stolen with permission from Daniel B. Cristofani] __________________________________ Yahoo! Mail - PC Magazine Editors' Choice 2005 http://mail.yahoo.com

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[math-fun] Found in the IHP cellar! 2/2
by Christian Boyer 21 Nov '05

21 Nov '05

---- FAUQUEMBERGUE computations And I have the chance to have discovered, again in the cellar of the Institut Henri Poincaré, the original handwritten computations on Mersenne numbers M101, M103, and M109 as sent by Fauquembergue to André Gérardin. http://www.utm.edu/research/primes/mersenne/LukeMirror/lit/lit_008s.htm These computations done in 1913-1914 were... false, as found by Robinson 40 years later: http://www.utm.edu/research/primes/mersenne/LukeMirror/lit/lit_024s.htm Within the huge number of handwritten 0s and 1s, the game would be to locate the first line where the error occurs! I can send .JPG photos to interested people. Christian.

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Re: [math-fun] sudoku
by dasimov＠earthlink.net 21 Nov '05

21 Nov '05

Thanks, Scott. >From the link you provided I see that another interesting question is, What is the smallest number n such that *every* sudoku solution can be reduced to n entries having that solution as its unique completion? Also: Is there a consensus about how to evaluate the "difficulty" of a given sudoku puzzle? (I was suprised to read at that URL that some feel that a large proportion of puzzles of least known size -- 17 -- are "easy".) --Dan ---------------------------------------------------------------------------------------- << >What is the smallest number of filled squares that >can uniquely determine an extension filling all >81 squares? > >--Dan There are many 17-clue sudokus known. The jury is still out whether a 16-clue sudoku exists. Specific sudoku grids which require 17+ clues are known. If you require rotational symmetry of initial clue positions I think 18-clues in the minumum known. Most of the 17-clue sudokus are not very difficult, so globally minimal clue count doesn't seem to correlate with difficulty. See http://www.sudoku.com/forums/viewtopic.php?t=605 for an extensive discussion. >>

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Re: [math-fun] math problem from the ISEE
by dasimov＠earthlink.net 21 Nov '05

21 Nov '05

I found the problem easy -- solved it in a yoctosecond. What do I think? I think it's appropriate for a middle school qualification test. (At first I thought, like Bernie, that the problem contradicted itself, that the mislabeled diagram couldn't be to scale. But that's wrong: the diagram represents the *cities* to scale. Nowhere does it claim to accurately depict all four distance labels.) --Dan

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[math-fun] Answer to the ISEE math problem
by Thane Plambeck 21 Nov '05

21 Nov '05

From "What to Expect from the ISEE", pg 39: * * * 10. This problem tells us that P, Q, R, and S are towns on the map. The distances between the towns are drawn to scale, which means they are as accurately drawn as possible. The distance between Town R and Town S is 13. For the distance between Town Q and Town S to be 26, the line segment QS should be twice as long as the line segment RS. Line segment QS is less than twice as long as line segment RS, so the distance between Town Q and Town S is not correct. The correct answer is choice (D). * * * -- Thane Plambeck http://www.plambeck.org/ehome.htm

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Re: [math-fun] math problem from the ISEE
by Jpr2718＠aol.com 21 Nov '05

21 Nov '05

Maybe the "13" could be "15". John Robertson _jpr2718(a)aol.com_ (mailto:jpr2718@aol.com)

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Re: [math-fun] math problem from the ISEE
by Jpr2718＠aol.com 21 Nov '05

21 Nov '05

Thane Plambeck wrote in part: I'm interested in what people may think of the following math problem from a document entitled "What to Expect on the ISEE." I hope they allowed rulers, with markings, and calculators! And I hope it was really printed to scale (as opposed to what was submitted to the printing company being to scale). With the JPG, who can tell. The "13" looks off the most from the rest (about 1.25 times the "12" as opposed to the expected ratio of 1.083). I printed it and measured to the nearest millimeter to get the following. Of course, I could be off a millimeter in my readings. Other printers or screens could give different results. By varying the aspect ratio, it looks like the "12" can be made to be in line with the "8" and "26", but there is no hope for the "13". Printed version (HP LaserJet 6): Dist mm Ratio 8 49 6.125 12 80 6.666666667 13 100 7.692307692 26 162 6.230769231 Measuring directly off the screen gave: Dist mm Ratio 8 44 5.5 12 70 5.833333333 13 89 6.846153846 26 144 5.538461538 John Robertson _jpr2718(a)aol.com_ (mailto:jpr2718@aol.com)

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[math-fun] math problem from the ISEE
by Thane Plambeck 21 Nov '05

21 Nov '05

I'm interested in what people may think of the following math problem from a document entitled "What to Expect on the ISEE." The ISEE is a widely-required exam for students applying to private middle schools in the US Sharpen your No. 2 pencils please, then click the URL below http://www.flickr.com/photos/thane/65247884/ -- Thane Plambeck http://www.plambeck.org/ehome.htm

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RE: [math-fun] maple? mathematica? or matlab OR magma ??
by dasimov＠earthlink.net 18 Nov '05

18 Nov '05

John McKay wrote: << . . . perhaps someone can tell us when numerical approximations are useful? . . . >> Sure: * When you're experimenting with concrete cases to try to find or confirm a pattern. * When for similar reasons you want to see a fairly accurate visual depiction of a mathematical object or of some statistics related to one. * When you want to display a result that cannot to your knowledge be expressed in closed form. (And, I'm sure, for many other reasons.) --Dan

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