# What's New -  October 2004

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October 26, 2004:   Pell's equation: given a positive integer N, find a positive integer y such that Ny2+1 is a perfect square. Not so easy unless you have a methodology.  Continued fractions provides a way to solve it for any non-square N.    As a byproduct, it also provides enough information to calculate the square root of N to any desired degree of accuracy.   That's enough to earn Pell and Continued Fractions a place over in the Math Topics section.   Although I haven't tried them all, this version should work for arbitrarily large numbers (within reason, N=9998 returns a 60 digit number for y.  If anyone checks it for accuracy, let me know the result  :>) .

October 20, 2004:  A viewer  recently sent the following inquiry.

how do you figure out how many times the clock hands are at a 90 % angle in a 24 hour period???? please respond, it's making me crazy!!
thanks

I sent this reply, but it also prompted me to update the Clock Angles program with  a button to answer the question visually.

October 13, 2004:   No new programs this week.  Well actually about  20 or 30 new programs but none to be posted here.   Here's the story:  Almost two years ago, in January 2003, I ran across  a great math and math programming problem site, Project Euler at MathsChallenge.net.   At the time there were 21  programming problems, set up with online scores and rankings posted.  I did them all and and posted a "10 Easy Pieces"  page that provide "last ditch" solutions for the  10  even numbered programs.

A viewer recently asked a question about problem number 66 (Pell's Equation)  that got me back to the site and hooked again.  There are now 83 problems to be solved and 700 enrolled users.   I've work my back up to 53 solved and  I'm now ranked 59th.  It is addictive!  The programs are now graded (based on number of correct solutions submitted) and so get more challenging as you progress.   Brute force is having less chance of succeeding for  the higher numbered programs and require some actual thought about program design.   Problem 54 involves scoring Poker hands - and haven't written it yet because I'm "cherry picking"  my way up the list, but it does sound like an interesting project.

In any event, I encourage any current or would-be recreational programmers to check it out.  I guarantee that you will learn something!   Besides, only 19 of the 700 members claim Delphi as their preferred language, although we do tend to be grouped in the upper half of the rankings (half of us are in the top 100) .   Two of the seven users that have solved all 83 programs  are Delphians!  Way to go guys!.

By the way, the Links page at MathsChallenge,net is the best I've seen for recreational math enthusiasts and other sections have graded math problems aimed at junior and high school students.

October 7, 2004:  I posted the promised update for the Crossword Puzzler Generator today.  It adds a Print Preview capability which also allows printed titles, save and restore of puzzle images,  and printable solutions for Word Search puzzles.  I also added a couple of additional word list files:  "German.txt"  (German words, English definitions to help our family prepare for our trip to Switzerland next spring), and "FieldsOfStudy.txt" with about 600 fields defined - makes one tough puzzle!

October 6, 2004:  Here's a semi-mathematical program demonstrating an enhanced version of our TComboSet unit which returns combinations and permutations when selecting  subsets from a set of N objects.    The revised version in Selection with Replacement,    adds the equivalent combinations and permutations when the item selected is not removed  (or removed and replaced before the next selection is made).  The analogy used is selecting labeled balls from a bag of balls.  Oh yeah, and if the ball labels are integers, the program will also select sets that sum to a given value.