How many digit number combinations fit this criteria?

Question

Question 1 Hi all. I need to find out what are the 4 digit number combinations that can add up to a final number of 6. For example: 6666 = 6+6+6+6 = 24 = 2+4 = 6

Question 2 Instead of using 4 digit combinations, what are the alternative 2 & 3 digit combinations that can add up to a final number of 6? For example: 33 = 3+3 = 6 (This is an example of a 2 digit combination)

Looking forward to your answers!

Answer 1

There are exactly 1000 4-digit combinations:

[1005, 1014, 1023, 1032, 1041, 1050, 1059, 1068, 1077, 1086, 1095, 1104, 1113, 1122, 1131, 1140, 1149, 1158, 1167, 1176, 1185, 1194, 1203, 1212, 1221, 1230, 1239, 1248, 1257, 1266, 1275, 1284, 1293, 1302, 1311, 1320, 1329, 1338, 1347, 1356, 1365, 1374, 1383, 1392, 1401, 1410, 1419, 1428, 1437, 1446, 1455, 1464, 1473, 1482, 1491, 1500, 1509, 1518, 1527, 1536, 1545, 1554, 1563, 1572, 1581, 1590, 1599, 1608, 1617, 1626, 1635, 1644, 1653, 1662, 1671, 1680, 1689, 1698, 1707, 1716, 1725, 1734, 1743, 1752, 1761, 1770, 1779, 1788, 1797, 1806, 1815, 1824, 1833, 1842, 1851, 1860, 1869, 1878, 1887, 1896, 1905, 1914, 1923, 1932, 1941, 1950, 1959, 1968, 1977, 1986, 1995, 2004, 2013, 2022, 2031, 2040, 2049, 2058, 2067, 2076, 2085, 2094, 2103, 2112, 2121, 2130, 2139, 2148, 2157, 2166, 2175, 2184, 2193, 2202, 2211, 2220, 2229, 2238, 2247, 2256, 2265, 2274, 2283, 2292, 2301, 2310, 2319, 2328, 2337, 2346, 2355, 2364, 2373, 2382, 2391, 2400, 2409, 2418, 2427, 2436, 2445, 2454, 2463, 2472, 2481, 2490, 2499, 2508, 2517, 2526, 2535, 2544, 2553, 2562, 2571, 2580, 2589, 2598, 2607, 2616, 2625, 2634, 2643, 2652, 2661, 2670, 2679, 2688, 2697, 2706, 2715, 2724, 2733, 2742, 2751, 2760, 2769, 2778, 2787, 2796, 2805, 2814, 2823, 2832, 2841, 2850, 2859, 2868, 2877, 2886, 2895, 2904, 2913, 2922, 2931, 2940, 2949, 2958, 2967, 2976, 2985, 2994, 3003, 3012, 3021, 3030, 3039, 3048, 3057, 3066, 3075, 3084, 3093, 3102, 3111, 3120, 3129, 3138, 3147, 3156, 3165, 3174, 3183, 3192, 3201, 3210, 3219, 3228, 3237, 3246, 3255, 3264, 3273, 3282, 3291, 3300, 3309, 3318, 3327, 3336, 3345, 3354, 3363, 3372, 3381, 3390, 3399, 3408, 3417, 3426, 3435, 3444, 3453, 3462, 3471, 3480, 3489, 3498, 3507, 3516, 3525, 3534, 3543, 3552, 3561, 3570, 3579, 3588, 3597, 3606, 3615, 3624, 3633, 3642, 3651, 3660, 3669, 3678, 3687, 3696, 3705, 3714, 3723, 3732, 3741, 3750, 3759, 3768, 3777, 3786, 3795, 3804, 3813, 3822, 3831, 3840, 3849, 3858, 3867, 3876, 3885, 3894, 3903, 3912, 3921, 3930, 3939, 3948, 3957, 3966, 3975, 3984, 3993, 4002, 4011, 4020, 4029, 4038, 4047, 4056, 4065, 4074, 4083, 4092, 4101, 4110, 4119, 4128, 4137, 4146, 4155, 4164, 4173, 4182, 4191, 4200, 4209, 4218, 4227, 4236, 4245, 4254, 4263, 4272, 4281, 4290, 4299, 4308, 4317, 4326, 4335, 4344, 4353, 4362, 4371, 4380, 4389, 4398, 4407, 4416, 4425, 4434, 4443, 4452, 4461, 4470, 4479, 4488, 4497, 4506, 4515, 4524, 4533, 4542, 4551, 4560, 4569, 4578, 4587, 4596, 4605, 4614, 4623, 4632, 4641, 4650, 4659, 4668, 4677, 4686, 4695, 4704, 4713, 4722, 4731, 4740, 4749, 4758, 4767, 4776, 4785, 4794, 4803, 4812, 4821, 4830, 4839, 4848, 4857, 4866, 4875, 4884, 4893, 4902, 4911, 4920, 4929, 4938, 4947, 4956, 4965, 4974, 4983, 4992, 5001, 5010, 5019, 5028, 5037, 5046, 5055, 5064, 5073, 5082, 5091, 5100, 5109, 5118, 5127, 5136, 5145, 5154, 5163, 5172, 5181, 5190, 5199, 5208, 5217, 5226, 5235, 5244, 5253, 5262, 5271, 5280, 5289, 5298, 5307, 5316, 5325, 5334, 5343, 5352, 5361, 5370, 5379, 5388, 5397, 5406, 5415, 5424, 5433, 5442, 5451, 5460, 5469, 5478, 5487, 5496, 5505, 5514, 5523, 5532, 5541, 5550, 5559, 5568, 5577, 5586, 5595, 5604, 5613, 5622, 5631, 5640, 5649, 5658, 5667, 5676, 5685, 5694, 5703, 5712, 5721, 5730, 5739, 5748, 5757, 5766, 5775, 5784, 5793, 5802, 5811, 5820, 5829, 5838, 5847, 5856, 5865, 5874, 5883, 5892, 5901, 5910, 5919, 5928, 5937, 5946, 5955, 5964, 5973, 5982, 5991, 6000, 6009, 6018, 6027, 6036, 6045, 6054, 6063, 6072, 6081, 6090, 6099, 6108, 6117, 6126, 6135, 6144, 6153, 6162, 6171, 6180, 6189, 6198, 6207, 6216, 6225, 6234, 6243, 6252, 6261, 6270, 6279, 6288, 6297, 6306, 6315, 6324, 6333, 6342, 6351, 6360, 6369, 6378, 6387, 6396, 6405, 6414, 6423, 6432, 6441, 6450, 6459, 6468, 6477, 6486, 6495, 6504, 6513, 6522, 6531, 6540, 6549, 6558, 6567, 6576, 6585, 6594, 6603, 6612, 6621, 6630, 6639, 6648, 6657, 6666, 6675, 6684, 6693, 6702, 6711, 6720, 6729, 6738, 6747, 6756, 6765, 6774, 6783, 6792, 6801, 6810, 6819, 6828, 6837, 6846, 6855, 6864, 6873, 6882, 6891, 6900, 6909, 6918, 6927, 6936, 6945, 6954, 6963, 6972, 6981, 6990, 6999, 7008, 7017, 7026, 7035, 7044, 7053, 7062, 7071, 7080, 7089, 7098, 7107, 7116, 7125, 7134, 7143, 7152, 7161, 7170, 7179, 7188, 7197, 7206, 7215, 7224, 7233, 7242, 7251, 7260, 7269, 7278, 7287, 7296, 7305, 7314, 7323, 7332, 7341, 7350, 7359, 7368, 7377, 7386, 7395, 7404, 7413, 7422, 7431, 7440, 7449, 7458, 7467, 7476, 7485, 7494, 7503, 7512, 7521, 7530, 7539, 7548, 7557, 7566, 7575, 7584, 7593, 7602, 7611, 7620, 7629, 7638, 7647, 7656, 7665, 7674, 7683, 7692, 7701, 7710, 7719, 7728, 7737, 7746, 7755, 7764, 7773, 7782, 7791, 7800, 7809, 7818, 7827, 7836, 7845, 7854, 7863, 7872, 7881, 7890, 7899, 7908, 7917, 7926, 7935, 7944, 7953, 7962, 7971, 7980, 7989, 7998, 8007, 8016, 8025, 8034, 8043, 8052, 8061, 8070, 8079, 8088, 8097, 8106, 8115, 8124, 8133, 8142, 8151, 8160, 8169, 8178, 8187, 8196, 8205, 8214, 8223, 8232, 8241, 8250, 8259, 8268, 8277, 8286, 8295, 8304, 8313, 8322, 8331, 8340, 8349, 8358, 8367, 8376, 8385, 8394, 8403, 8412, 8421, 8430, 8439, 8448, 8457, 8466, 8475, 8484, 8493, 8502, 8511, 8520, 8529, 8538, 8547, 8556, 8565, 8574, 8583, 8592, 8601, 8610, 8619, 8628, 8637, 8646, 8655, 8664, 8673, 8682, 8691, 8700, 8709, 8718, 8727, 8736, 8745, 8754, 8763, 8772, 8781, 8790, 8799, 8808, 8817, 8826, 8835, 8844, 8853, 8862, 8871, 8880, 8889, 8898, 8907, 8916, 8925, 8934, 8943, 8952, 8961, 8970, 8979, 8988, 8997, 9006, 9015, 9024, 9033, 9042, 9051, 9060, 9069, 9078, 9087, 9096, 9105, 9114, 9123, 9132, 9141, 9150, 9159, 9168, 9177, 9186, 9195, 9204, 9213, 9222, 9231, 9240, 9249, 9258, 9267, 9276, 9285, 9294, 9303, 9312, 9321, 9330, 9339, 9348, 9357, 9366, 9375, 9384, 9393, 9402, 9411, 9420, 9429, 9438, 9447, 9456, 9465, 9474, 9483, 9492, 9501, 9510, 9519, 9528, 9537, 9546, 9555, 9564, 9573, 9582, 9591, 9600, 9609, 9618, 9627, 9636, 9645, 9654, 9663, 9672, 9681, 9690, 9699, 9708, 9717, 9726, 9735, 9744, 9753, 9762, 9771, 9780, 9789, 9798, 9807, 9816, 9825, 9834, 9843, 9852, 9861, 9870, 9879, 9888, 9897, 9906, 9915, 9924, 9933, 9942, 9951, 9960, 9969, 9978, 9987, 9996]

...and exactly 100 3-digit combinations:

[105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402, 411, 420, 429, 438, 447, 456, 465, 474, 483, 492, 501, 510, 519, 528, 537, 546, 555, 564, 573, 582, 591, 600, 609, 618, 627, 636, 645, 654, 663, 672, 681, 690, 699, 708, 717, 726, 735, 744, 753, 762, 771, 780, 789, 798, 807, 816, 825, 834, 843, 852, 861, 870, 879, 888, 897, 906, 915, 924, 933, 942, 951, 960, 969, 978, 987, 996]

...and exactly 10 2-digit combinations:

[15, 24, 33, 42, 51, 60, 69, 78, 87, 96]