Cages with 1 squares

Total

Combinations

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

Cages with 2 squares

Total

Combinations

3

12

4

13

5

14
23

6

15
24

7

16
25
34

8

17
26
35

9

18
27
36
45

10

19
28
37
46

11

29
38
47
56

12

39
48
57

13

49
58
67

14

59
68

15

69
78

16

79

17

89

Cages with 3 squares

Total

Combinations

6

123

7

124

8

125
134

9

126
135
234

10

127
136
145
235

11

128
137
146
236
245

12

129
138
147
156
237
246
345

13

139
148
157
238
247
256
346

14

149
158
167
239
248
257
347
356

15

159
168
249
258
267
348
357
456

16

169
178
259
268
349
358
367
457

17

179
269
278
359
368
458
467

18

189
279
369
378
459
468
567

19

289
379
469
478
568

20

389
479
569
578

21

489
579
678

22

589
679

23

689

24

789

Cages with 4 squares

Total

Combinations

10

1234

11

1235

12

1236
1245

13

1237
1246
1345

14

1238
1247
1256
1346
2345

15

1239
1248
1257
1347
1356
2346

16

1249
1258
1267
1348
1357
1456
2347
2356

17

1259
1268
1349
1358
1367
1457
2348
2357
2456

18

1269
1278
1359
1368
1458
1467
2349
2358
2367
2457
3456

19

1279
1369
1378
1459
1468
1567
2359
2368
2458
2467
3457

20

1289
1379
1469
1478
1568
2369
2378
2459
2468
2567
3458
3467

21

1389
1479
1569
1578
2379
2469
2478
2568
3459
3468
3567

22

1489
1579
1678
2389
2479
2569
2578
3469
3478
3568
4567

23

1589
1679
2489
2579
2678
3479
3569
3578
4568

24

1689
2589
2679
3489
3579
3678
4569
4578

25

1789
2689
3589
3679
4579
4678

26

2789
3689
4589
4679
5678

27

3789
4689
5679

28

4789
5689

29

5789

30

6789

Cages with 5 squares

Total

Combinations

15

12345

16

12346

17

12347
12356

18

12348
12357
12456

19

12349
12358
12367
12457
13456

20

12359
12368
12458
12467
13457
23456

21

12369
12378
12459
12468
12567
13458
13467
23457

22

12379
12469
12478
12568
13459
13468
13567
23458
23467

23

12389
12479
12569
12578
13469
13478
13568
14567
23459
23468
23567

24

12489
12579
12678
13479
13569
13578
14568
23469
23478
23568
24567

25

12589
12679
13489
13579
13678
14569
14578
23479
23569
23578
24568
34567

26

12689
13589
13679
14579
14678
23489
23579
23678
24569
24578
34568

27

12789
13689
14589
14679
15678
23589
23679
24579
24678
34569
34578

28

13789
14689
15679
23689
24589
24679
25678
34579
34678

29

14789
15689
23789
24689
25679
34589
34679
35678

30

15789
24789
25689
34689
35679
45678

31

16789
25789
34789
35689
45679

32

26789
35789
45689

33

36789
45789

34

46789

35

56789

Cages with 6 squares

Total

Combinations

21

123456

22

123457

23

123458
123467

24

123459
123468
123567

25

123469
123478
123568
124567

26

123479
123569
123578
124568
134567

27

123489
123579
123678
124569
124578
134568
234567

28

123589
123679
124579
124678
134569
134578
234568

29

123689
124589
124679
125678
134579
134678
234569
234578

30

123789
124689
125679
134589
134679
135678
234579
234678

31

124789
125689
134689
135679
145678
234589
234679
235678

32

125789
134789
135689
145679
234689
235679
245678

33

126789
135789
145689
234789
235689
245679
345678

34

136789
145789
235789
245689
345679

35

146789
236789
245789
345689

36

156789
246789
345789

37

256789
346789

38

356789

39

456789

Cages with 7 squares

Total

Combinations

28

1234567

29

1234568

30

1234569
1234578

31

1234579
1234678

32

1234589
1234679
1235678

33

1234689
1235679
1245678

34

1234789
1235689
1245679
1345678

35

1235789
1245689
1345679
2345678

36

1236789
1245789
1345689
2345679

37

1246789
1345789
2345689

38

1256789
1346789
2345789

39

1356789
2346789

40

1456789
2356789

41

2456789

42

3456789

Cages with 8 squares

Total

Combinations

36

12345678

37

12345679

38

12345689

39

12345789

40

12346789

41

12356789

42

12456789

43

13456789

44

23456789

Cages with 9 squares

Total

Combinations

45

123456789