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Summer Teacher Institute

TEAM 5. super computing challenge. Summer Teacher Institute. JUNE 28, 2001. Tess F. Ballard Cherie O’Dell Ron Payton Rita Pino-Vargas. ONE FOR ALL. Pattern Analysis of Sums with Unique Integers. historical connection. Agusta Ada Byron Lovelace.

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Summer Teacher Institute

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  1. TEAM 5 supercomputingchallenge Summer Teacher Institute JUNE 28, 2001 Tess F. Ballard Cherie O’Dell Ron Payton Rita Pino-Vargas

  2. ONE FOR ALL Pattern Analysis of Sums with Unique Integers

  3. historical connection Agusta Ada Byron Lovelace English mathematician credited for developing binary arithmetic. Binary arithmetic was used 100 years later in the design of computers.

  4. problem What special patterns can be found among the valid addition expression of the form of A+B=C, such that each digit from one (1) to nine (9) is used exactly once in A,B or C? 124 659 ---- 783

  5. hypothesis If a set of such sums are found, patterns will exist among them.

  6. process * Computer Program listing 3-digit numbers of the form a + b = c such that all the digits 1 through 9 are represented among a, b, & c. * Cast out any duplicate sums due to communitivity. * Look for patterns that have similar answers. * Find commonalities of all such sums . * Improve program * Extend Program to to include Base 13 and Base 16.

  7. theorems Every sum has exactly one (1) carry. The carry must occur in 1’s or 10’s column.

  8. code Development and implementation • 1st C Program • Slow (10mins) • Rendered both Valid and Invalid Sums • output bulky (500 pages)

  9. code (continued) • 2nd C Program • Faster (almost instantly) • Valid output only • Output streamlined to 3 pages • Uses brute force • Not as efficient • Not portable to other numbers

  10. code (continued) • Pascal Program • Output down to one (1) page • Uses less Brute Force • Coding more efficient and and cleaner • Portable to any number base

  11. results Base 10 168 possible combinations of addends were found. Total of digits in answer always equals 18 Program terminated after 333 total Base 13 answer always 33 or 39 Base 16 answer always equals 60

  12. conclusion Proved two theorems Solved original problem Extended process to Base 13 and Base 16 Designed better programs and More efficient algorithms Satisfied the hypothesis

  13. recommendations Translate program to C or C++ Formulate a proof as to why the sums always equal to a constant.

  14. acknowledgments Dr. Curtis Barefoot Gina Fiske David Kratzer Eric Ovaska

  15. references Dover, Gandmier. Mathematics, Magic and Mystery. Martin Press ,1956. Edward, Kasner. Mathematics and the Imagination. Schusterand Simon ,1967. Kline,Morris. Mathematics and the Search for Knowledge. Oxford Univ. Press,1985 http://www.well.com/user/adatoole/bio.htm http://www.geocities.com/Vienna/3941/thelist.html http://www.seanet.com/~ksbrown/htt 06/20/2001 http://www.ceismc.gatech.edu/busyt/math.html 06/26/2001 http://www.loc.gov/06/26/2001

  16. benefits • Acquiring new research skills • Team work • Time management • Organizational Skills • Followed the Scientific Process • Experienced the use of Technology • experienced computer programming

  17. The work begins when the presentation is over... THIS PRESENTATION IS OVER

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