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Let's guess puzzle 69, how long will it take to solve this problem?Six months, one year, three years or even longer.
Regarding prefixes:Is it faster to use the birthday argument to find hash160?Has anyone paid attention to this?

I can do it in 29671 days, I only need around 10 $ every day, to keep a steady rate. I'm already at 0.003276% of the scan. Are you in?

Yes, you can definitely force the H160 values/prefixes to repeat to your liking so that birthday argument applies. It's totally wrong to think that the birthday paradox simply applies for two people sharing the same birthday, whichever birthday it may be. It of course applies to two people that share the exact birthday you want them to have. Your mentor / ocult clan leader that obliges you people to pollute this thread every time the air starts to clean itself up, is spot on!

i dont understand how we imply the birthday paradox in kangaroo method how is a random jumps will yield the same point at some STEP

The analysis of the Kangaroo method does not use the birthday paradox. Close but not exactly. The math behind it is clearly explained in many papers.

But this has nothing to do with address-only puzzles, which are simply brute-force problems. Anything else than this, if proven, automatically implies that secp256k1, SHA, and RIPEMD are all broken, since their cryptographic guarantees would be thrown at the trash.

Terminology question : isn’t birthday paradox the search of collision of 2 subsets of size sqrt(n) ?
If so I don’t really get how kangaroo is different ? By different do you mean implementation details like DP etc… or something else ?

You can't know if the unknown kangaroos are inside the set, or they exited it, so you can't apply b-day paradox to that analysis. Besides, it's not like a jump can select any element with equal chances, as it only goes forward, and it also has a maximum jump size.

B-day paradox is used by Gaudry-Schost method (which uses sets), not by Kangaroo. RC's Kangaroo is not technically a Kangaroo method.

Ok I learned about GS before kangaroos hence my confusion in the terminology. Not an expert there anyway

what is GS or is it you mean baby-step_giant-step