10958 is a Hard Problem!
I was talking to my nephew Jack-Jack the other day about the 10958 Ascending debacle. If you are unfamiliar with it, check out my post from 10/21/19. It is a nasty little piece of ostensibly simple math.
Jack-Jack and I were trying to find an answer to the 10958 problem when I told him what I always do when faced with a math problem that is very hard. Simply put, I give up. In my experience, that is almost always the best way forward. Does that mean I go to bed and forget about the problem? No, not at all. I will use 10958 Ascending to illustrate what I mean.
Look over the following numbers, and you will quickly see what the problem is all about. The numbers 1 thru 9 have to be used in ascending order. You can use the simple mathematical operators, along with exponents and parentheses. Obviously, the equation you create has to equal 10958.
I told Jack-Jack that the problem appears to be too difficult to solve. People have been looking for an answer for a long time and everyone has come up empty. I suggested we do the following: Let’s take 10958 and multiply it by 9 and then divide that number by 8.
In terms of the numbers we have to worry about, the problem has just gotten much easier. Now we only have to deal with 7 numbers instead of 9. That is a big difference. By giving up on the original problem we may have found an easier route to a solution. And yes, I am not too happy about the decimal. The “.75” may very well create more problems than it solves.
Of course, we can keep working backward in the hopes of finding a solution. Will that work? I doubt it. The more I look at this problem, the more convinced I am that there is no solution. Why so pessimistic? Many professional mathematicians have written computer programs to search for an answer. None has been found.
In general, though, I believe that giving up on hard problems is a sound strategy. If the problem can be broken down into smaller, more easily manageable parts, then the chances for a solution go up. In this particular case, I think we are all up against it. We are left with trying to figure out what is so special about 10958. It appears to me to be just another number except in this particular instance. I really don’t know what to think about this issue. It is all very strange.
Postscript
So, it took me a long time to get this posted. I was in the hospital for about 5 days. I am fine. I am feeling a lot better and things are looking good for my future. One of the doctors told me I should have another 40 years as long as I don’t get hit by a dump truck while out for a run.
During my stay, I spent a lot of time on the 10958 problem. I would have done a lot of writing but when I left for my doctor’s appointment I was too weak to walk upstairs and get my laptop. I had a suspicion I was going to the hospital, and I really wanted my laptop, but I didn’t want to be found three weeks later in a pile at the bottom of the stairs.
As you might guess, I made no progress on the problem. I truly find it astonishing that solutions to every other number up to 11111 are easily found. What is special about 10958? Why is it out there on a limb by itself? I still have no idea. I remain confused.
(1 − 2 + 3) × (456 + 7! − 8 − 9)
Mr. Bushkin,
I was stunned to see your solution. I hadn’t seen it before. I sent the equation to Professor Inder Taneja, the author of the original paper on the topic, and he said he was familiar with the result. Apparently, the factorial is not welcome. I am disappointed; I was hopeful that your work would count as a solution. Well done, even though you are scuttled by a technicality! (of course, I had to end with an !)
RTNM
I also found the solution that Mr Bushkin found.
The first webpage I saw, that describes this problem, did list factorials as an operation that could be used, but I. Taneja has not put this as a solution.
He has also not said that there is no solution possible, even after computers cannot find a solution
I have found another solution that uses basic operations, but it requires one decimal point.