ENOVATIVE NUMBER PLACEMENT SUDOKU LECTURE 4

Hung-ping Tsao (2026). Enovative Number Placement Sudoku Lecture 4. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Lawrence K. Wang and Hung-ping Tsao (editors). Volume 8, Number 5D, May 2026; 40 pages. Lenox Institute Press MA, USA. ABSTRACT: • Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used. Hard puzzles can sometimes be solved by the construction of strategic flipflops. • The purpose of this lecture series is for you to have a new prospective in playing Sudoku. In addition to the introduction of efficient methods, we most importantly stress on the number placement aspect of Sudoku. • We shall try to solve most of the hard puzzles from ULTIMATE 600 PUZZLES and Wayne Gould's 200 Difficult Su Doku puzzles for this lecture series. • Readers are adviced to consult LECTURE 0 for self-explanatory moves in the figures. Careful readers might be able to discern that Wayne Gould's puzzles are more rational, which would be a challenge to pinpoint! • We introduce innovative cross reference moves for solving flipflops and tripleflips. • We add a new feature of hidden numbers bazaar. Keywords: Number Placement, Sudoku, Rational Puzzle, Row move, Column move, Block move, Box move, Grid move, Terminating move, Rule of unique solution, Candidate, Principle of the Least Choice, Residue, Flipflops chain, Stratigic flipflops, Cross reference moves for flipflops and tripleflips, Hidden numbers bazaar.