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I have not heard of cage or sandwich methods, but I'll look into them. btw, I just ordered a Qiyi 5x5 so in a few days I'll find out whether M slices still work at that size or not.

5x5 M slices are clunky, but possible. Bigger they get tougher. Of course you can always stimulate M slices with R, L and x. I never bothered to learn R U Z- and H-perms, and once solved a 10x10 with I think a Z-perm.
 
I need help with some 4x4 last layer I think this might be a parity but not sure still new to 4x4 the picture below is my problem. The pieces out of place are the only pieces keeping the puzzle from being solved
 

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I need help with some 4x4 last layer I think this might be a parity but not sure still new to 4x4 the picture below is my problem. The pieces out of place are the only pieces keeping the puzzle from being solved

Edge pairing isn't finished. You should finish edge pairing before starting 3x3 stage. In this case there are a couple of easy ways to fix this:
-You can put the unsolved edges in the FR and FL slots such that green-yellow is on top and red-yellow is on the bottom, or vice versa, then Uw' [flip FR edge] Uw.
-Rw2 D Rw' U2 Rw D' Rw' U2 Rw' *2
-Reverse the above algorithm, but only do it once. The only reason I would do it twice is that it's a 2-look OLL that I know performed with wide turns, and I'm too lazy to learn new algs.
 
I never tried solving anything above a 3x3, and plan to get a 4x4 to start learning.
As a total newb in 4x4s (never touched one before), should I get a high-end 4x4 like an AoSu or Wuque from the start, or start on a budget shengshou 4x4?
Thanks.
 
I never tried solving anything above a 3x3, and plan to get a 4x4 to start learning.
As a total newb in 4x4s (never touched one before), should I get a high-end 4x4 like an AoSu or Wuque from the start, or start on a budget shengshou 4x4?
Thanks.

(Disclaimer: this is an opinion.) Go for the high-end cube if you can afford it, unless you're getting it just as a collector. The modern premium 4×4×4s are significantly better than the budget cubes, and if you decide to get a budget cube only to realise it turns like crap, you basically just wasted whatever you spent on it.
 
I never tried solving anything above a 3x3, and plan to get a 4x4 to start learning.
As a total newb in 4x4s (never touched one before), should I get a high-end 4x4 like an AoSu or Wuque from the start, or start on a budget shengshou 4x4?
Thanks.

I'm personally thrilled right now with my DIY magnetic Yuxin Blue, but the Cyclone Boys G4 has a low-mid price point ($12 on theCubicle, $4.89 from Lightake or MCM) and in my opinion is very competitive in terms of turning quality. It may, however, be the only cube I've actually worn out. The core does not have an especially robust design. I got mine used, and it was an instant main over my Aosu, but rumor has it that it needs a fair bit of break in before it stops being catchy. Otherwise it is fantastic. That would be my recommendation.
 
So I have been trying to get Sub-1 on 4x4 for quite some time, and I can't seem to get there. I have had a few Sub-1 singles, but not an average. I use the Yau method, and I average 16 seconds on 3x3. Any help?
 
I doubt if Hoya can help.

I'm also trying to get in 1min mark. I'm quite fluent with Hoya and I get similar time using Hoya and Yau. I guess Hoya only helps if you're not color neutral, and you have a case where non-white/yellow centers are super easy to pair up. In terms of move-count and look-ahead, Hoya is at best similar to Yau if not slightly worse.
 
Practise your PLL and OLL parity(at least sub-1.5 for first and sub-4 for second). Fast two centres will help but for YAU, first three cross edges are more tricky to find pairs. Which last four centres you're using? Half centers or each center individually? But for me what helped most - lube your cube. Fast cube makes you sub-1 easily
 
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