But one little nagging problem I had was that, while I knew there was a finite limit as to how far you could go with each chain, I had no idea what that limit actually was. So it was possible to spend hours racking your brain trying to come up with a solution that was mathematically impossible. From this, I got the idea to run computer simulations on all possible games to achieve a maximum score for each one, and created this search engine to let you know exactly what score you should be shooting for!

A couple of months ago, I discovered the Number Ladder Game, a fun little way to pass time on the Internet in the Number Jugglers site. I became obsessed with playing the Super Challenge, a simple yet desceptive and interesting challenge. The rules for the Super Challenge are simple: you are randomly given five numbers from 1 to 9. Using all five numbers you try to write an equation using only addition, subtraction, multiplication, division, and parenthesis to get the value of 1. If successful, you try to find a value of 2, then 3, and 4, and so on. You keep this UP as long as you can, until you cannot find an equation using all five numbers that extends the chain.I played this game for a while, and got quite good at it. But one little nagging problem I had was that, while I knew there was a finite limit as to how far you could go with each chain, I had no idea what that limit actually was. So it was possible to spend hours racking your brain trying to come up with a solution that was mathematically impossible. From this, I got the idea to run computer simulations on all possible games to achieve a maximum score for each one, and created this search engine to let you know exactly what score you should be shooting for! Simply enter in the five numbers for your game in the form below, click the submit button, and you will receive the perfect score possible for your Super Challenge. If you are stuck and want to know the solution, there is also a link to other page with a sample of one chain of equations that will give you a perfect score (but it is more fun if you try your best on your own before resorting to looking at the answers!) For those of you who are curious, the highest perfect score possible for the Challenge is 261 equations for the numbers 4 5 6 7 9, the highest perfect score possible for the Super Challenge is 192 for the numbers 4 5 6 7 8. Many thanks to Ruth Bell Alexander for making this fun game available to us all! Note: These results are only tested for the Super Challenge level, not the normal Challenge. If you are interested in a search engine for the Challenge level, please contact me. If enough people show interest, maybe I'll do one for that as well...
