Sequence combinations

Question

I am trying to find all possibilities of a 4 digit code using the numbers 1 thru 6. the same number can be used for any of the four (i.e. 1, 1, 1, 1).

Answer 1

6 raised to the 4th power

6 choices * 6 choices * 6 choices * 6 choices

Answer 2

Here they are:

1111 1112 1113 1114 1115 1116 1121 1122 1123 1124 1125 1126 1131 1132 1133 1134 1135 1136 1141 1142 1143 1144 1145 1146 1151 1152 1153 1154 1155 1156 1161 1162 1163 1164 1165 1166 1211 1212 1213 1214 1215 1216 1221 1222 1223 1224 1225 1226 1231 1232 1233 1234 1235 1236 1241 1242 1243 1244 1245 1246 1251 1252 1253 1254 1255 1256 1261 1262 1263 1264 1265 1266 1311 1312 1313 1314 1315 1316 1321 1322 1323 1324 1325 1326 1331 1332 1333 1334 1335 1336 1341 1342 1343 1344 1345 1346 1351 1352 1353 1354 1355 1356 1361 1362 1363 1364 1365 1366 1411 1412 1413 1414 1415 1416 1421 1422 1423 1424 1425 1426 1431 1432 1433 1434 1435 1436 1441 1442 1443 1444 1445 1446 1451 1452 1453 1454 1455 1456 1461 1462 1463 1464 1465 1466 1511 1512 1513 1514 1515 1516 1521 1522 1523 1524 1525 1526 1531 1532 1533 1534 1535 1536 1541 1542 1543 1544 1545 1546 1551 1552 1553 1554 1555 1556 1561 1562 1563 1564 1565 1566 1611 1612 1613 1614 1615 1616 1621 1622 1623 1624 1625 1626 1631 1632 1633 1634 1635 1636 1641 1642 1643 1644 1645 1646 1651 1652 1653 1654 1655 1656 1661 1662 1663 1664 1665 1666 2111 2112 2113 2114 2115 2116 2121 2122 2123 2124 2125 2126 2131 2132 2133 2134 2135 2136 2141 2142 2143 2144 2145 2146 2151 2152 2153 2154 2155 2156 2161 2162 2163 2164 2165 2166 2211 2212 2213 2214 2215 2216 2221 2222 2223 2224 2225 2226 2231 2232 2233 2234 2235 2236 2241 2242 2243 2244 2245 2246 2251 2252 2253 2254 2255 2256 2261 2262 2263 2264 2265 2266 2311 2312 2313 2314 2315 2316 2321 2322 2323 2324 2325 2326 2331 2332 2333 2334 2335 2336 2341 2342 2343 2344 2345 2346 2351 2352 2353 2354 2355 2356 2361 2362 2363 2364 2365 2366 2411 2412 2413 2414 2415 2416 2421 2422 2423 2424 2425 2426 2431 2432 2433 2434 2435 2436 2441 2442 2443 2444 2445 2446 2451 2452 2453 2454 2455 2456 2461 2462 2463 2464 2465 2466 2511 2512 2513 2514 2515 2516 2521 2522 2523 2524 2525 2526 2531 2532 2533 2534 2535 2536 2541 2542 2543 2544 2545 2546 2551 2552 2553 2554 2555 2556 2561 2562 2563 2564 2565 2566 2611 2612 2613 2614 2615 2616 2621 2622 2623 2624 2625 2626 2631 2632 2633 2634 2635 2636 2641 2642 2643 2644 2645 2646 2651 2652 2653 2654 2655 2656 2661 2662 2663 2664 2665 2666 3111 3112 3113 3114 3115 3116 3121 3122 3123 3124 3125 3126 3131 3132 3133 3134 3135 3136 3141 3142 3143 3144 3145 3146 3151 3152 3153 3154 3155 3156 3161 3162 3163 3164 3165 3166 3211 3212 3213 3214 3215 3216 3221 3222 3223 3224 3225 3226 3231 3232 3233 3234 3235 3236 3241 3242 3243 3244 3245 3246 3251 3252 3253 3254 3255 3256 3261 3262 3263 3264 3265 3266 3311 3312 3313 3314 3315 3316 3321 3322 3323 3324 3325 3326 3331 3332 3333 3334 3335 3336 3341 3342 3343 3344 3345 3346 3351 3352 3353 3354 3355 3356 3361 3362 3363 3364 3365 3366 3411 3412 3413 3414 3415 3416 3421 3422 3423 3424 3425 3426 3431 3432 3433 3434 3435 3436 3441 3442 3443 3444 3445 3446 3451 3452 3453 3454 3455 3456 3461 3462 3463 3464 3465 3466 3511 3512 3513 3514 3515 3516 3521 3522 3523 3524 3525 3526 3531 3532 3533 3534 3535 3536 3541 3542 3543 3544 3545 3546 3551 3552 3553 3554 3555 3556 3561 3562 3563 3564 3565 3566 3611 3612 3613 3614 3615 3616 3621 3622 3623 3624 3625 3626 3631 3632 3633 3634 3635 3636 3641 3642 3643 3644 3645 3646 3651 3652 3653 3654 3655 3656 3661 3662 3663 3664 3665 3666 4111 4112 4113 4114 4115 4116 4121 4122 4123 4124 4125 4126 4131 4132 4133 4134 4135 4136 4141 4142 4143 4144 4145 4146 4151 4152 4153 4154 4155 4156 4161 4162 4163 4164 4165 4166 4211 4212 4213 4214 4215 4216 4221 4222 4223 4224 4225 4226 4231 4232 4233 4234 4235 4236 4241 4242 4243 4244 4245 4246 4251 4252 4253 4254 4255 4256 4261 4262 4263 4264 4265 4266 4311 4312 4313 4314 4315 4316 4321 4322 4323 4324 4325 4326 4331 4332 4333 4334 4335 4336 4341 4342 4343 4344 4345 4346 4351 4352 4353 4354 4355 4356 4361 4362 4363 4364 4365 4366 4411 4412 4413 4414 4415 4416 4421 4422 4423 4424 4425 4426 4431 4432 4433 4434 4435 4436 4441 4442 4443 4444 4445 4446 4451 4452 4453 4454 4455 4456 4461 4462 4463 4464 4465 4466 4511 4512 4513 4514 4515 4516 4521 4522 4523 4524 4525 4526 4531 4532 4533 4534 4535 4536 4541 4542 4543 4544 4545 4546 4551 4552 4553 4554 4555 4556 4561 4562 4563 4564 4565 4566 4611 4612 4613 4614 4615 4616 4621 4622 4623 4624 4625 4626 4631 4632 4633 4634 4635 4636 4641 4642 4643 4644 4645 4646 4651 4652 4653 4654 4655 4656 4661 4662 4663 4664 4665 4666 5111 5112 5113 5114 5115 5116 5121 5122 5123 5124 5125 5126 5131 5132 5133 5134 5135 5136 5141 5142 5143 5144 5145 5146 5151 5152 5153 5154 5155 5156 5161 5162 5163 5164 5165 5166 5211 5212 5213 5214 5215 5216 5221 5222 5223 5224 5225 5226 5231 5232 5233 5234 5235 5236 5241 5242 5243 5244 5245 5246 5251 5252 5253 5254 5255 5256 5261 5262 5263 5264 5265 5266 5311 5312 5313 5314 5315 5316 5321 5322 5323 5324 5325 5326 5331 5332 5333 5334 5335 5336 5341 5342 5343 5344 5345 5346 5351 5352 5353 5354 5355 5356 5361 5362 5363 5364 5365 5366 5411 5412 5413 5414 5415 5416 5421 5422 5423 5424 5425 5426 5431 5432 5433 5434 5435 5436 5441 5442 5443 5444 5445 5446 5451 5452 5453 5454 5455 5456 5461 5462 5463 5464 5465 5466 5511 5512 5513 5514 5515 5516 5521 5522 5523 5524 5525 5526 5531 5532 5533 5534 5535 5536 5541 5542 5543 5544 5545 5546 5551 5552 5553 5554 5555 5556 5561 5562 5563 5564 5565 5566 5611 5612 5613 5614 5615 5616 5621 5622 5623 5624 5625 5626 5631 5632 5633 5634 5635 5636 5641 5642 5643 5644 5645 5646 5651 5652 5653 5654 5655 5656 5661 5662 5663 5664 5665 5666 6111 6112 6113 6114 6115 6116 6121 6122 6123 6124 6125 6126 6131 6132 6133 6134 6135 6136 6141 6142 6143 6144 6145 6146 6151 6152 6153 6154 6155 6156 6161 6162 6163 6164 6165 6166 6211 6212 6213 6214 6215 6216 6221 6222 6223 6224 6225 6226 6231 6232 6233 6234 6235 6236 6241 6242 6243 6244 6245 6246 6251 6252 6253 6254 6255 6256 6261 6262 6263 6264 6265 6266 6311 6312 6313 6314 6315 6316 6321 6322 6323 6324 6325 6326 6331 6332 6333 6334 6335 6336 6341 6342 6343 6344 6345 6346 6351 6352 6353 6354 6355 6356 6361 6362 6363 6364 6365 6366 6411 6412 6413 6414 6415 6416 6421 6422 6423 6424 6425 6426 6431 6432 6433 6434 6435 6436 6441 6442 6443 6444 6445 6446 6451 6452 6453 6454 6455 6456 6461 6462 6463 6464 6465 6466 6511 6512 6513 6514 6515 6516 6521 6522 6523 6524 6525 6526 6531 6532 6533 6534 6535 6536 6541 6542 6543 6544 6545 6546 6551 6552 6553 6554 6555 6556 6561 6562 6563 6564 6565 6566 6611 6612 6613 6614 6615 6616 6621 6622 6623 6624 6625 6626 6631 6632 6633 6634 6635 6636 6641 6642 6643 6644 6645 6646 6651 6652 6653 6654 6655 6656 6661 6662 6663 6664 6665 6666

Answer 3

Which, just in case your calculator is broken = 1296

I don't know what the underlying requirement or application is, but allowing 0 (zero's) would almost double the number of possible combinations, to 2401 (7 x 7 x 7 x 7).

Answer 4

Is the question really for the number of permutations? This sounds suspiciously like the number of combinations possible when throwing dice. So maybe the question is for the number of combinations with repetition. Which ... I think is (6+4-1)! / ((4!)(6-1)!) = 126. Or I might be wrong, that class was many years in the past.

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Answer 5

What exactly are you trying to find? If you are looking for the number of different combinations, then you can find it like so:
For the first number you have 6 possibilities, for the second number you also have 6 possibilities, and same for the third and fourth numbers. So this gives you 6 x 6 x 6 x 6 possibilities (= 6 ^ 4 = 1296).

If you are trying to print all the numbers out, you can use a number of nested loops. The algorithm for this is classed as O(n^4), since the time it takes to execute is ~4x the size of your input (in this case six, the number of possibilities). Using pseudo code, you could do something like this:

max ⟵ 6
for count1 ⟵ 1 to max do
    for count2 ⟵ 1 to max do
        for count3 ⟵ 1 to max do
            for count4 ⟵ 1 to max do
                print count1, count2, count3, count4

This will give you a list equivalent to that produced by John Rasch (note that this pseudo-code will not compile in any language that I know of, but you should be easily able to translate it into your language of choice).

Answer 6

If you don't want the nested loops, just count from 0 to 6^4 - 1 (or 7^4 - 1 on Sunday) and convert to base 6 (or 7).