If you're even more clever and try the "open switch between each key press", you similarly don't have to try "12" because it's a prefix of "123". Likewise, you don't have to try "1" because it's a prefix of "123". With that in mind, there are 512 "combinations."

So, with that said, if you try the "open" button for every "*", and reset for every "->", your sequence is:

0 * ->
1 * 0 * ->
2 * 0 * ->
3 * 0 * ->
4 * 0 * ->
5 * 0 * ->
6 * 0 * ->
7 * 0 * ->
8 * 0 * ->
9 * 0 * ->
12 * 0 * ->
13 * 0 * ->
14 * 0 * ->
15 * 0 * ->
16 * 0 * ->
17 * 0 * ->
18 * 0 * ->
19 * 0 * ->
23 * 0 * ->
24 * 0 * ->
25 * 0 * ->
26 * 0 * ->
27 * 0 * ->
28 * 0 * ->
29 * 0 * ->
34 * 0 * ->
35 * 0 * ->
36 * 0 * ->
37 * 0 * ->
38 * 0 * ->
39 * 0 * ->
45 * 0 * ->
46 * 0 * ->
47 * 0 * ->
48 * 0 * ->
49 * 0 * ->
56 * 0 * ->
57 * 0 * ->
58 * 0 * ->
59 * 0 * ->
67 * 0 * ->
68 * 0 * ->
69 * 0 * ->
78 * 0 * ->
79 * 0 * ->
89 * 0 * ->
123 * 0 * ->
124 * 0 * ->
125 * 0 * ->
126 * 0 * ->
127 * 0 * ->
128 * 0 * ->
129 * 0 * ->
134 * 0 * ->
135 * 0 * ->
136 * 0 * ->
137 * 0 * ->
138 * 0 * ->
139 * 0 * ->
145 * 0 * ->
146 * 0 * ->
147 * 0 * ->
148 * 0 * ->
149 * 0 * ->
156 * 0 * ->
157 * 0 * ->
158 * 0 * ->
159 * 0 * ->
167 * 0 * ->
168 * 0 * ->
169 * 0 * ->
178 * 0 * ->
179 * 0 * ->
189 * 0 * ->
234 * 0 * ->
235 * 0 * ->
236 * 0 * ->
237 * 0 * ->
238 * 0 * ->
239 * 0 * ->
245 * 0 * ->
246 * 0 * ->
247 * 0 * ->
248 * 0 * ->
249 * 0 * ->
256 * 0 * ->
257 * 0 * ->
258 * 0 * ->
259 * 0 * ->
267 * 0 * ->
268 * 0 * ->
269 * 0 * ->
278 * 0 * ->
279 * 0 * ->
289 * 0 * ->
345 * 0 * ->
346 * 0 * ->
347 * 0 * ->
348 * 0 * ->
349 * 0 * ->
356 * 0 * ->
357 * 0 * ->
358 * 0 * ->
359 * 0 * ->
367 * 0 * ->
368 * 0 * ->
369 * 0 * ->
378 * 0 * ->
379 * 0 * ->
389 * 0 * ->
456 * 0 * ->
457 * 0 * ->
458 * 0 * ->
459 * 0 * ->
467 * 0 * ->
468 * 0 * ->
469 * 0 * ->
478 * 0 * ->
479 * 0 * ->
489 * 0 * ->
567 * 0 * ->
568 * 0 * ->
569 * 0 * ->
578 * 0 * ->
579 * 0 * ->
589 * 0 * ->
678 * 0 * ->
679 * 0 * ->
689 * 0 * ->
789 * 0 * ->
1234 * 0 * ->
1235 * 0 * ->
1236 * 0 * ->
1237 * 0 * ->
1238 * 0 * ->
1239 * 0 * ->
1245 * 0 * ->
1246 * 0 * ->
1247 * 0 * ->
1248 * 0 * ->
1249 * 0 * ->
1256 * 0 * ->
1257 * 0 * ->
1258 * 0 * ->
1259 * 0 * ->
1267 * 0 * ->
1268 * 0 * ->
1269 * 0 * ->
1278 * 0 * ->
1279 * 0 * ->
1289 * 0 * ->
1345 * 0 * ->
1346 * 0 * ->
1347 * 0 * ->
1348 * 0 * ->
1349 * 0 * ->
1356 * 0 * ->
1357 * 0 * ->
1358 * 0 * ->
1359 * 0 * ->
1367 * 0 * ->
1368 * 0 * ->
1369 * 0 * ->
1378 * 0 * ->
1379 * 0 * ->
1389 * 0 * ->
1456 * 0 * ->
1457 * 0 * ->
1458 * 0 * ->
1459 * 0 * ->
1467 * 0 * ->
1468 * 0 * ->
1469 * 0 * ->
1478 * 0 * ->
1479 * 0 * ->
1489 * 0 * ->
1567 * 0 * ->
1568 * 0 * ->
1569 * 0 * ->
1578 * 0 * ->
1579 * 0 * ->
1589 * 0 * ->
1678 * 0 * ->
1679 * 0 * ->
1689 * 0 * ->
1789 * 0 * ->
2345 * 0 * ->
2346 * 0 * ->
2347 * 0 * ->
2348 * 0 * ->
2349 * 0 * ->
2356 * 0 * ->
2357 * 0 * ->
2358 * 0 * ->
2359 * 0 * ->
2367 * 0 * ->
2368 * 0 * ->
2369 * 0 * ->
2378 * 0 * ->
2379 * 0 * ->
2389 * 0 * ->
2456 * 0 * ->
2457 * 0 * ->
2458 * 0 * ->
2459 * 0 * ->
2467 * 0 * ->
2468 * 0 * ->
2469 * 0 * ->
2478 * 0 * ->
2479 * 0 * ->
2489 * 0 * ->
2567 * 0 * ->
2568 * 0 * ->
2569 * 0 * ->
2578 * 0 * ->
2579 * 0 * ->
2589 * 0 * ->
2678 * 0 * ->
2679 * 0 * ->
2689 * 0 * ->
2789 * 0 * ->
3456 * 0 * ->
3457 * 0 * ->
3458 * 0 * ->
3459 * 0 * ->
3467 * 0 * ->
3468 * 0 * ->
3469 * 0 * ->
3478 * 0 * ->
3479 * 0 * ->
3489 * 0 * ->
3567 * 0 * ->
3568 * 0 * ->
3569 * 0 * ->
3578 * 0 * ->
3579 * 0 * ->
3589 * 0 * ->
3678 * 0 * ->
3679 * 0 * ->
3689 * 0 * ->
3789 * 0 * ->
4567 * 0 * ->
4568 * 0 * ->
4569 * 0 * ->
4578 * 0 * ->
4579 * 0 * ->
4589 * 0 * ->
4678 * 0 * ->
4679 * 0 * ->
4689 * 0 * ->
4789 * 0 * ->
5678 * 0 * ->
5679 * 0 * ->
5689 * 0 * ->
5789 * 0 * ->
6789 * 0 * ->
12345 * 0 * ->
12346 * 0 * ->
12347 * 0 * ->
12348 * 0 * ->
12349 * 0 * ->
12356 * 0 * ->
12357 * 0 * ->
12358 * 0 * ->
12359 * 0 * ->
12367 * 0 * ->
12368 * 0 * ->
12369 * 0 * ->
12378 * 0 * ->
12379 * 0 * ->
12389 * 0 * ->
12456 * 0 * ->
12457 * 0 * ->
12458 * 0 * ->
12459 * 0 * ->
12467 * 0 * ->
12468 * 0 * ->
12469 * 0 * ->
12478 * 0 * ->
12479 * 0 * ->
12489 * 0 * ->
12567 * 0 * ->
12568 * 0 * ->
12569 * 0 * ->
12578 * 0 * ->
12579 * 0 * ->
12589 * 0 * ->
12678 * 0 * ->
12679 * 0 * ->
12689 * 0 * ->
12789 * 0 * ->
13456 * 0 * ->
13457 * 0 * ->
13458 * 0 * ->
13459 * 0 * ->
13467 * 0 * ->
13468 * 0 * ->
13469 * 0 * ->
13478 * 0 * ->
13479 * 0 * ->
13489 * 0 * ->
13567 * 0 * ->
13568 * 0 * ->
13569 * 0 * ->
13578 * 0 * ->
13579 * 0 * ->
13589 * 0 * ->
13678 * 0 * ->
13679 * 0 * ->
13689 * 0 * ->
13789 * 0 * ->
14567 * 0 * ->
14568 * 0 * ->
14569 * 0 * ->
14578 * 0 * ->
14579 * 0 * ->
14589 * 0 * ->
14678 * 0 * ->
14679 * 0 * ->
14689 * 0 * ->
14789 * 0 * ->
15678 * 0 * ->
15679 * 0 * ->
15689 * 0 * ->
15789 * 0 * ->
16789 * 0 * ->
23456 * 0 * ->
23457 * 0 * ->
23458 * 0 * ->
23459 * 0 * ->
23467 * 0 * ->
23468 * 0 * ->
23469 * 0 * ->
23478 * 0 * ->
23479 * 0 * ->
23489 * 0 * ->
23567 * 0 * ->
23568 * 0 * ->
23569 * 0 * ->
23578 * 0 * ->
23579 * 0 * ->
23589 * 0 * ->
23678 * 0 * ->
23679 * 0 * ->
23689 * 0 * ->
23789 * 0 * ->
24567 * 0 * ->
24568 * 0 * ->
24569 * 0 * ->
24578 * 0 * ->
24579 * 0 * ->
24589 * 0 * ->
24678 * 0 * ->
24679 * 0 * ->
24689 * 0 * ->
24789 * 0 * ->
25678 * 0 * ->
25679 * 0 * ->
25689 * 0 * ->
25789 * 0 * ->
26789 * 0 * ->
34567 * 0 * ->
34568 * 0 * ->
34569 * 0 * ->
34578 * 0 * ->
34579 * 0 * ->
34589 * 0 * ->
34678 * 0 * ->
34679 * 0 * ->
34689 * 0 * ->
34789 * 0 * ->
35678 * 0 * ->
35679 * 0 * ->
35689 * 0 * ->
35789 * 0 * ->
36789 * 0 * ->
45678 * 0 * ->
45679 * 0 * ->
45689 * 0 * ->
45789 * 0 * ->
46789 * 0 * ->
56789 * 0 * ->
123456 * 0 * ->
123457 * 0 * ->
123458 * 0 * ->
123459 * 0 * ->
123467 * 0 * ->
123468 * 0 * ->
123469 * 0 * ->
123478 * 0 * ->
123479 * 0 * ->
123489 * 0 * ->
123567 * 0 * ->
123568 * 0 * ->
123569 * 0 * ->
123578 * 0 * ->
123579 * 0 * ->
123589 * 0 * ->
123678 * 0 * ->
123679 * 0 * ->
123689 * 0 * ->
123789 * 0 * ->
124567 * 0 * ->
124568 * 0 * ->
124569 * 0 * ->
124578 * 0 * ->
124579 * 0 * ->
124589 * 0 * ->
124678 * 0 * ->
124679 * 0 * ->
124689 * 0 * ->
124789 * 0 * ->
125678 * 0 * ->
125679 * 0 * ->
125689 * 0 * ->
125789 * 0 * ->
126789 * 0 * ->
134567 * 0 * ->
134568 * 0 * ->
134569 * 0 * ->
134578 * 0 * ->
134579 * 0 * ->
134589 * 0 * ->
134678 * 0 * ->
134679 * 0 * ->
134689 * 0 * ->
134789 * 0 * ->
135678 * 0 * ->
135679 * 0 * ->
135689 * 0 * ->
135789 * 0 * ->
136789 * 0 * ->
145678 * 0 * ->
145679 * 0 * ->
145689 * 0 * ->
145789 * 0 * ->
146789 * 0 * ->
156789 * 0 * ->
234567 * 0 * ->
234568 * 0 * ->
234569 * 0 * ->
234578 * 0 * ->
234579 * 0 * ->
234589 * 0 * ->
234678 * 0 * ->
234679 * 0 * ->
234689 * 0 * ->
234789 * 0 * ->
235678 * 0 * ->
235679 * 0 * ->
235689 * 0 * ->
235789 * 0 * ->
236789 * 0 * ->
245678 * 0 * ->
245679 * 0 * ->
245689 * 0 * ->
245789 * 0 * ->
246789 * 0 * ->
256789 * 0 * ->
345678 * 0 * ->
345679 * 0 * ->
345689 * 0 * ->
345789 * 0 * ->
346789 * 0 * ->
356789 * 0 * ->
456789 * 0 * ->
1234567 * 0 * ->
1234568 * 0 * ->
1234569 * 0 * ->
1234578 * 0 * ->
1234579 * 0 * ->
1234589 * 0 * ->
1234678 * 0 * ->
1234679 * 0 * ->
1234689 * 0 * ->
1234789 * 0 * ->
1235678 * 0 * ->
1235679 * 0 * ->
1235689 * 0 * ->
1235789 * 0 * ->
1236789 * 0 * ->
1245678 * 0 * ->
1245679 * 0 * ->
1245689 * 0 * ->
1245789 * 0 * ->
1246789 * 0 * ->
1256789 * 0 * ->
1345678 * 0 * ->
1345679 * 0 * ->
1345689 * 0 * ->
1345789 * 0 * ->
1346789 * 0 * ->
1356789 * 0 * ->
1456789 * 0 * ->
2345678 * 0 * ->
2345679 * 0 * ->
2345689 * 0 * ->
2345789 * 0 * ->
2346789 * 0 * ->
2356789 * 0 * ->
2456789 * 0 * ->
3456789 * 0 * ->
12345678 * 0 * ->
12345679 * 0 * ->
12345689 * 0 * ->
12345789 * 0 * ->
12346789 * 0 * ->
12356789 * 0 * ->
12456789 * 0 * ->
13456789 * 0 * ->
23456789 * 0 * ->
123456789 * 0 * ->