December 07, 2018
dr dan friesen headshot

UNT Dallas assistant dean of the School of Business Dr. Daniel Friesen co-authored an article that was recently published in Business Management Dynamics.

The piece, titled “A Model of Sam Loyd’s Outwitting the Weighing Machine,” appeared in the publication’s August edition. It considers alternative solution methods for the puzzle, “Outwitting the Weighing Machine,” by Sam Loyd -- an American chess player, puzzle author and recreational mathematician who died in 1911 -- by using Excel Solver and LINGO for this and other challenging problems.

Dr. Friesen and co-author Dr. Mike Patterson, a professor at Midwestern State University’s Dillard College of Business Administration, are former colleagues at the Wichita Falls institution, and have collaborated on journal articles for a dozen years.

“I enjoy writing the story and background while Mike enjoys creating and improving the models,” Dr. Friesen said. “Through our collaboration, we have addressed several of the puzzles and games that are popular topics in ‘recreational mathematics,’ ‘recreational programming’ and ‘recreational computer science,’ including Sudoku, The Monty Hall problem, Einstein’s Riddle and Sam Loyd’s Mars Canals Maze.

“Spreadsheets are a wonderful tool for approaching modeling,” Dr. Friesen continued, “especially if you aren’t well-grounded in a programming language.”

In case you’re wondering about the answer to Sam Loyd’s puzzle originally issued in the early 20th Century, but have no clue how to begin the mathematical equations necessary to solve such a riddle, well, the weights of the young girls are 56, 58, 60, 64 and 65 pounds.

In summary, Friesen and Patterson write: “Puzzles and riddles, such as Sam Loyd’s ‘Outwitting the Weighing Machine,’ provide exercises in logic and mathematical reasoning. The puzzle, written some 100 years ago, was undoubtedly designed as a pencil-and-paper exercise. However, it can be modeled and solved using readily available software, such as Excel Solver and LINGO. The software models in this paper illustrate that ‘Outwitting the Weighing Machine’ would provide the basis for a challenging learning exercise for any operations research-oriented class.”

Congratulations to Dr. Friesen and Dr. Patterson.