2x2x2 cube
             q+h    loc max            q only    loc max
 0:            1          -                 1          -
 1:            9          -                 6          -
 2:           54          -                27          -
 3:          321          -               120          -
 4:         1847         11               534          -
 5:         9992          8              2256          -
 6:        50136         96              8969          -
 7:       227536        904             33058         16
 8:       870072      13212            114149         53
 9:      1887748     413392            360508        260
10:       623800     604516            930588       1460
11:         2644       2644           1350852      34088
12:                                    782536     402260
13:                                     90280      88636
14:                                       276        276

3x3x3 corners only
             q+h    loc max            q only    loc max
 0:            1          -                 1          -
 1:           18          -                12          -
 2:          243          -               114          -
 3:         2874          6               924          -
 4:        28000         88              6539          -
 5:       205416        792             39528          -
 6:      1168516      15304            199926        114
 7:      5402628      46068            806136        600
 8:     20776176     325680           2761740      17916
 9:     45391616    9757376           8656152      10200
10:     15139616   14665856          22334112      35040
11:        64736      64736          32420448     818112
12:                                  18780864    9654240
13:                                   2166720    2127264
14:                                      6624       6624

magic domino, 1 solution
             q+h    loc max            q only    loc max
 0:            1          -                 1          -
 1:           10          -                 8          -
 2:           67          -                48          -
 3:          420          -               260          -
 4:         2335          -              1330          -
 5:        12260          -              6556          -
 6:        61038          3             31301          -
 7:       291004         12            144392          -
 8:      1327429        793            638407          2
 9:      5821374       6170           2709620         64
10:     24141784      87202          10873023       1261
11:     89480354     990826          39768668      15728
12:    262907144   13212972         124815946     214530
13:    485409604   91824956         296531984    2741192
14:    508704668  161596512         460831364   23949864
15:    232904952  175407548         435219080   72423024
16:     14508468   13668852         215035460   91647012
17:       129376     128592          38469576   35228568
18:          112        112            624320     618368
19:                                      1056       1056

magic domino, 4 solutions
             q+h    loc max            q only    loc max
 0:            4          -                 4          -
 1:           28          -                24          -
 2:          136          -               108          -
 3:          672          -               480          -
 4:         3228          -              2116          -
 5:        15072          -              9120          -
 6:        69000          -             39188          -
 7:       310784         92            166408          -
 8:      1369220       1052            691508         56
 9:      5888676       8656           2812496        192
10:     24209988      92284          11015008       1860
11:     89458152     976008          39837904      16104
12:    262772436   13124304         124673780     202940
13:    485358148   91776620         296336800    2667824
14:    508703948  161595792         460769708   23896632
15:    232904952  175407548         435217336   72421280
16:     14508468   13668852         215035460   91647012
17:       129376     128592          38469576   35228568
18:          112        112            624320     618368
19:                                      1056       1056

magic domino, 8 solutions
             q+h    loc max            q only    loc max
 0:            8          -                 8          -
 1:           56          -                48          -
 2:          272          -               216          -
 3:         1344          -               960          -
 4:         6456          -              4232          -
 5:        30144          -             18240          -
 6:       138000          -             78376          -
 7:       621568        184            332816          -
 8:      2732664       3096           1383016        112
 9:     11649816      28672           5612576        384
10:     46553800     331960          21772432       4584
11:    158726064    3909520          75752384      47792
12:    377277280   46692640         208971608     783864
13:    507933248  129847936         388348544   11790688
14:    414571632  181149888         466373488   54544928
15:    102181280   86967456         334811104   78445984
16:      3271456    3221680         114248208   79836432
17:         7312       7312           7974528    7869280
18:                                     19616      19616