What is the maximum tooth sprocket you could fit on the back using a Deore DX rear derailleur?

I notice people like to discourage me from tinkering as they think I am not qualified to do it

if you are ok with potentially having to undo stuff or further fettle to make it work then fine - tinker away! For sure its a a good way to learn

I think the sense of 'discouragement' is because at times you've been given overly specific information about 'what to do' which you seem to have latched on to, and with all due respect, without really giving the impression you've really understood the context well enough or know about about how all this stuff works generally with all the different standards and what works with what to be able to successfully wrangle what you think you want.

You do you of course, but I think myself and many others are a little sceptical about your aims. My first MTB in the late 80s had a bog standard MTB triple up front, with a 22 granny ring, a 7 speed cassette with a max 28T cog, and it could climb literally ANYTHING. Of course I was a teenager at the time and if stuff got hard (and it did) you just had to peddle harder :)

The idea that one would actually need a 20T granny and a 36/40T back sprocket to climb steep but not technical terrain just seems a bit weird, or indicative of being unfit and unused to cycling. You seem to want to setup a bike to climb potentially steep, but non technical hills, VERY VERY slowly - Are you sure YOU are really the 'hill climber' you think you want to be ?- cos I think it's much more about YOU than the bike!

its not unusual to get caught up in the "fantasy" of something (especially if one has maybe a little OCD!) and find the actual reality disappointing. I know I do - I often get more out of looking at, and building and fettling bikes than actually riding them ;)

I'm not saying any of this to be unkind BTW, I recognise some of myself in your approach here for sure :)
 
To put all this in context - in the olden times people would win the Tour de France, which at that point in history had brutally long and steep mountain stages on unpaved roads, on SINGLE SPEED bikes!!!

those guys were "Hill Climbers" :)
 
The idea that one would actually need a 20T granny and a 36/40T back sprocket to climb steep but not technical terrain just seems a bit weird, or indicative of being unfit and unused to cycling. You seem to want to setup a bike to climb potentially steep, but non technical hills, VERY VERY slowly - Are you sure YOU are really the 'hill climber' you think you want to be ?- cos I think it's much more about YOU than the bike!
Nothing to do with 'need'. I am allowed to have low gears if I want and that is what I want.

I could probably manage to get up most hills on a single speed (I am not the fat slob you are implying) but I definitely wouldn't enjoy it.

I find the idea of low gears fun. Not sure why it is such a big deal.

I had 18 gear inches as lowest before, it was pretty good. I now have 14 and like it more. I think I am old enough to know what I like and don't like.

I have ridden a bike on and off many years of my life so I am not as naive as you think about my goals.

Looking at the many threads on the internet about granny gears there are many more who feel the same so it isn't like it is some super niche idea.

Cycling is not about pure athletics that you make it out to be. Not for me anyway and not for many other cyclists. Exercise is part but for me just as interesting is tinkering and then trying out what I did. Also being outside in the countryside. None of that has anything to do with riding the hardest and highest gearing that your fitness will allow.
 
22/40 one imagines. A very nice low/low option, and at around 14"-ish you are probably where the author of the thread hopes to be.
11-40 with an ‘95 LX
On my ride today I played around with her. Going up a short steep section I normally do in 22/27 (equivalent to the original gearing) I used 11/40. Worked great.
Tonight on the stand I heard some noise. I have the B screw all the way in and it’s marginal. I had bought some derailleur extentions so threw one on. They work. I still have to figure out how to orient the extension.
Before and after (pardon the filth it’s a working bike)
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Nothing to do with 'need'. I am allowed to have low gears if I want and that is what I want.

I could probably manage to get up most hills on a single speed (I am not the fat slob you are implying) but I definitely wouldn't enjoy it.

I find the idea of low gears fun. Not sure why it is such a big deal.

I had 18 gear inches as lowest before, it was pretty good. I now have 14 and like it more. I think I am old enough to know what I like and don't like.

I have ridden a bike on and off many years of my life so I am not as naive as you think about my goals.

Looking at the many threads on the internet about granny gears there are many more who feel the same so it isn't like it is some super niche idea.

Cycling is not about pure athletics that you make it out to be. Not for me anyway and not for many other cyclists. Exercise is part but for me just as interesting is tinkering and then trying out what I did. Also being outside in the countryside. None of that has anything to do with riding the hardest and highest gearing that your fitness will allow.

don't take it so personally chief - I know text isn't often a great way to get 'tone of voice' correct but as I was at pains to point out, I was not intending to be cruel or unkind. I didn't say or imply you were either a 'fat slob' nor that cycling has to be particularly 'athletic' :)

However the reality is it does require some fitness to be enjoyable - especially where hills are involved. I'm absolutely calling the kettle black here. I'm not that fit myself and usually my approach to long steep hills is to avoid them :)

as I said, you do you. If it's what you want then go for it.
 
22/40 one imagines. A very nice low/low option, and at around 14"-ish you are probably where the author of the thread hopes to be.
I no longer need to hope, I have achieved it and ridden it. I have tasted the fruit of the gods.

I did run the numbers and 22/40 is almost identical to 20/36.

I find the pushback about low gearing peculiar. I don't see people complaining at people riding e-bikes which takes away much more of the physical aspect. Seems some subconscious issues about all the low gear shaming. Maybe e-bikes are so far removed as to not be a threat.
 
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To put all this in context - in the olden times people would win the Tour de France, which at that point in history had brutally long and steep mountain stages on unpaved roads, on SINGLE SPEED bikes!!!

those guys were "Hill Climbers" :)
The context is actually much more like the breadth of cycling done; as we are a broad church here. Inclusive. Everything from trials to track cycling. I can tell you that 14" is useful occasionally; especially in the scenario you have a big load and are pulling off.
 
you have a big load and are pulling off.

loaded up, touring style I can get it :)

I think there is a sort of law of diminishing returns at the low end though. In the MTB golden age 22 x 28 was 'enough' for pretty much anything if you had the legs - and even then that felt pretty spinny to the point you were on the verge of being unable to maintain enough forward momentum due to lack of speed. Does going ultra low to around 1:2 sort of ratio's really buy you much extra functionality, given you'd already be going very slowly? (I guess the OP would say "YES"!)

I can imagine its easier to peddle, but also even harder to keep up any sort of momentum that keeps you rolling. Anyway, each to their own!
 
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