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A little bit of an update post. The game is actually possible to beat with no jumps under these rules. (2 if spike jumps are illegal)

I explain this in a different comment, but basically wait until the strawberry in 1700 is at its lowest, fall into it, timing it such that you can dash up and collect it in the same frame. You will get another dash, so dash up again, spike jump, then its a success.

Edit: You can dash-jump instead of spike jumping

So actually this was impossible, I couldn’t do it. Was impossible. I literally just figured out a way to do it.

The problem with 1700 was that everything is just high enough where dash-grace jumps don’t gain enough height to finish the level, and ofc the speedrun strategy jumps by necessity.

What I noticed was that there’s a strawberry here, and a strawberry hitboxes move. Because of the position of the strawberry, you are able to pop open the box, wait for the strawberry to move to its lowest point, then intercept it. You need to fall into the strawberry, but time it so that you collect the strawberry and dash up in almost the same frame, which will give you a free extra dash. Dash up again, spike clip, and then etc

Surprisingly consistent. Uses a spike jump, but this is a victory nonetheless

Edit: You can skip the spike jump by dash-jumping instead

This one jump will haunt me, I think.

Brilliant 1900M method, much easier than mine. Very nice!

That's really cool, good find!

That's the first thing I tried, but the only times I could get to that layer was from accidently grace jumping, not wall jumping. Maybe you mistook a grace jump for a wall jump? 

Yea this challenge is fun

It's  a bit tight, but in 400m you can also get here without jumping, but I couldn't get to the strawberry without an extra jump, so that was a bust, but it does open up some new options

Edit: also a slightly easier way to do old site

Very nice!

I decided to try it without dash grace jumps and managed to lower it to 2, 1 in 1300, 1 in 1700, and 1 in 2600...

In 1100 it's possible to do a spike jump on that leftmost side and then continue as normal

In 1800, it's very tight, but you can just barely reach that first balloon by getting to it at it's lowest pixel

And in 2300 you are able to do the same trick as before

Also it might be possible to get one off of 2600, but I'm not sure, I keep dying at the brown X in the image
EDIT: Wait... you could do the gemskip strategy to beat it... give me a bit to do that
EDIT 2: did it

It's kinda hilarious to me that I missed those simpler solutions and chose much more annoying solutions like in 2400 and 1900 lol, thanks for those

I managed to lower it down to 0, I suspect your jump was on 1500m? You can do a spike walljump there and just barely reach the end. Nice job otherwise!

im a better gamer than the dev, no shield needed lol

I have never laughed at a game so hard... I am in tears lol, thank you

Nope, coyote jumps don't count, but coyote jumping out of a dash does count.

Edit: Other way around oops
You are not allowed to coyote jump, but you are allowed to coyote jump out of a dash.

I got 47 as well(wow). I got 5 jumps on 1900, but I think that one can be lowered.

Edit: Probably not :C
Edit: Here are all of my jumps on each level

100: 1
3
2
0
3
3
1
1
1
4
4
0
2
1
2
2
2
2
5?
0
0
1
1
3
0
0
3
0
0
0

Boom, video complete

Lol, just recently I lowered it down to 1, maybe I will make a video on it now

After playing for a while, I managed to beat the game in just 3 jumps. 

First of all, what's a jump?
Pressing jump on the ground is jump. Grace jumping is also a jump.
Grace jumping from a dash is not a jump though, so you can do that.
Wall jumping is not a jump.
And jumping on a spike is not a jump.

With these rules, you can beat the game with just 3 jumps.
This is not a tutorial on how to do it, but if people want to see how, I can make a video on it.

Good luck?

Edit: I lowered it down to 1 jump, so yay have fun
Edit2: Video guide: 

Edit3, feb 2024: Lowered it to 0!!