More illegal clusters

I've been a little curious with the illegal cluster concept, so I made these puzzles. It shouldn't be hard to solve, but hopefully it is fun. I think these are solid.

As a reminder: An illegal cluster is an illegal position that would be legal if ANY one unit (other than K) is removed.

1) Add a black knight, black bishop and a black rook to form an illegal cluster. [#Note - Cook found by Remellion. Move Kd4 to c3]

(b) Ka1 to b2

2) Add a black knight, black bishop, black rook and a black queen to form an illegal cluster.

3) Add a black pawn, black knight, black bishop, black rook and a black queen to form an illegal cluster (two solutions).

1a: multiple solutions +bNd2, +bBc3, +bRf1 (g1/h1) - position can be reflected in the diagonal a1-h8 too.

1b: +bNc2, +bBc1, +bRd2.

The others I haven't the time to do now - these can be quite hard.

Good job on 1a - you found unintended solutions! I missed the knight blocking the discovered check. Can you find the intended solution for 1a with the black king on c3?

1b - Solved!

I'll be glad to hear about your opinion on 2. and 3. when you have time. They look tricky but you can solve them not by trial and error, but instead by coming up with a certain strategy (it works on both 2. and 3.)

1a fixed: +bNb2, +bBa3, +bRa2. Interesting how it can't be mirrored or put further back.

1a - Solved. Well done.

p.s. If anyone has a source or a link for illegal clusters, I would be interested 

For 2 and 3 is it back to the original position with wKa1 and bKd4? Or progressive twinning?

Nop, it is as per the diagram, or progressive twinning if you will. If I could fit everything into a single diagram it would be great, but I can't 

The diagram appears just below the stipulation. I edited in bigger gaps to make it clear.

2) seems to be:

This type of pattern is oft used when looking for cooks. I call them 'bucket' cooks - place a piece such that it checks a K, then block its retractions in every direction. These, however, seem like intentional 'buckets' and it's instructive that they seemingly can be done only one way (though there is an aphorism of 'all ICs are cooked').

2) Solved. That is indeed the intended solution, well done!

No fancy ideas implemented here. I only searched for a setup that yields but one unique solution. If you change the position of the white king (for instance, b2), other "bucket" tries work, such as checking with the queen and blocking her escape routes (try queen on b1, block a2 c2 and d1).

Now that you reached thus far, solving 3) should be right around the corner. Can you find the two unique solutions, or otherwise prove me wrong???

Correct, good job once again!

3) Solved.

I suppose I'll post future illegal clusters in this thread.

I just made another, which should be pretty simple (also, a little bit of reused themes), yet I find the full solution elegant.

Add a Bp, BN and a BR to form an illegal cluster.

(b) Kh4 ---> g3

(c) Kh4 ---> h2

Good job. The idea is obviously to get a different piece to deliver check every time.

I'll see if I can make more interesting ones.

I wonder if this works...

Kinda obvious though.

Add a WB, WN, and two BRs to form an illegal cluster.

This, right?

But yeah, pretty obvious. The only piece that required a bit of thought was the added wN.

Removing the wNh1 does not relieve the illegality (white has no freedom), so it wouldn't work as an IC.

It's not quite that simple - w/o Nh1, -1...Rh1xRg1 -2.Kf1 fxNe1=R -3.Nd3 and it's Black who lacks the freedom. But you are correct that it is not an IC.