ok, I "stickied" this thread as well, so it'll always be at the top :)

Good evening, everyone. I've been reading the description for volume IV of the Advanced Calcudoku series, and I thought you guys might like some OR tables with zeroes. The original tables were kindly posted by clm a while back, so I just wanted to give credit where credit is due. A word of caution - I made NO distinction between L-shaped and in-line 3-cell cages as clm did with the original OR tables. That said, I've got some revised bitwise OR combinations below.

2 cells

1| 01
2| 02
3| 03 12 13 23
4| 04
5| 05 14 15 45
6| 06 24 26 46
7| 07 16 17 25 27 34 35 36 37 47 56 57 67
8| 08
9| 18
10| 28
11| 38
12| 48
13| 58
14| 68
15| 78

3 cells

1| 001 011
2| 002 022
3| 003 012 013 023 033 112 113 122 123 133 223 233
4| 004 044
5| 005 014 015 045 055 114 115 144 145 155 445 455
6| 006 024 026 046 066 224 226 244 246 266 446 466

7| 007 016 017 025 027 034 035 036 037 047 056 057 067 077 116 117 124 125 126 127 134 135 136
137 146 147 156 157 166 167 177 225 227 234 235 236 237 245 247 255 256 257 267 277 334 335
336 337 344 345 346 347 355 356 357 366 367 377 447 456 457 467 477 556 557 566 567 577 667
677

8| 008 088
9| 018 118 188
10| 028 228 288
11| 038 128 138 238 338 388
12| 048 448 488
13| 058 148 158 458 558 588
14| 068 248 268 468 668 688
15| 078 168 178 258 278 348 358 368 378 478 568 578 678 778 788

I will not go into detail as to how the bitwise OR operator works, since clm has already done just that.

Anyhow, I hope these tables give you guys a boost with the book puzzles.

Nice guide!

I was just thinking about writing a guide for the bitwise OR operation, but this thread deems that mostly unnecessary.
However, I would like to add one perspective that I often take on cages with 3|, 5| and 6|.
As clm rightly points out, these only have few combinations which go in to it. Taking 3|-cage as an example, you will see from the list of combinations that only 1's, 2's and 3's may go in to such a cage. However, it gets a bit better: any combination of 1's, 2's and 3's will actually work.
This means that, once you see a cage with 3| in it, you can pencil-mark 1's, 2's and 3's in ever cell of the cage. Once you've done that, you can completely ignore the cage itself. By this I mean: you have extracted all the information there is from the 3|-cage, and you won't need think about the actual cage again.
The exact same works for 5| (but this time with 1's, 4's and 5's) and for 6| (with 2's, 4's and 6's).
If you don't like thinking about bitwise OR operation (which I don't think anybody does), this may simplify things a bit.