For those of you who like The Four Fours Game, I just uploaded the newest version of my document dedicated to this obsession. It's part of this old thread I started for the previous version of the document: https://community.ptc.com/t5/PTC-Mathcad/Lusk-Four-Fours-Game-20120125-pdf/m-p/449748
I have to confess that my first thought on seeing the problem was "This looks like something a permutation generator would be nicely suited to chewing through the possibilities". Fortunately, I have far too many other things to keep me occupied.
Thanks. I prepared this updated version partly at the request of my mother...well, actually, I finished it much earlier than I had planned to meet her request. Mom is 85 years old, was a math major in college, did substitute teaching for high school trig and calculus for years, and still does math puzzles and logic puzzles for fun. She is prepping for her 67th high school reunion next month and had recently told two of her classmates (both retired high school math teachers) about my Four Fours document and each asked for a copy. Between 2012 and early 2021, as I had time to work on it, I added quite a bit to the document, greatly expanding the Introduction section and adding many new solutions. However, the document still wasn't ready to release when she asked me for copies in late August. I was only half done with solutions from 301 to 400, and had barely started creating and typing solutions for 401 to 500. Since 500 was my goal for this release, I had a lot left to do in only a few weeks. So, instead of doing the yard work my wife claimed was calling me, I finished Version 4. 🙂 Fortunately, when I am "in the zone", solutions come pretty quickly.
BTW, I have read accounts online about people who have written programs to do what you suggest. Here are two examples, although the second one is not really a Four Fours solvers, but I suspect the techniques are transferable: https://codegolf.stackexchange.com/questions/12063/four-fours-puzzle https://gist.github.com/Radcliffe/fab1cefe6e2a3a23466539a7ecbc6edb However, I think it's more fun to discover solutions by hand.
That's even more impressive, Fred! I hope you have similar excuses for avoiding yard work for many years to come.
I'm avoiding reading about other solutions to programming the Four Fours problem because where would be the fun in seeing how it was done? 😈
(I'm also wondering if I could generalize it to find solutions to the 'n' 'm's problem ...)
Still, the world is safe from such a putative program, as I have lots of grasshoppers in my 'zone', meaning I have an Earth-girdling chain of unfinished worksheets (I've got ten on the go at the moment, split between two laptops. Maybe it's just as well PTC doesn't make a Mac version of Mathcad).