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Counting Numbers with a Given Digit Sum

Posted: Sun May 09, 2021 11:24 pm
by Sujoy Mollick
How many four-digit numbers are there with digit sum equal to \(10\)?

চার অঙ্কের কয়টি সংখ্যা আছে যাদের অঙ্কের যোগফল \(10\)?

Re: Counting Numbers with a Given Digit Sum

Posted: Wed Aug 18, 2021 10:30 am
by 103568
Sujoy Mollick wrote:
Sun May 09, 2021 11:24 pm
How many four-digit numbers are there with digit sum equal to \(10\)?

চার অঙ্কের কয়টি সংখ্যা আছে যাদের অঙ্কের যোগফল \(10\)?
There are 219 such 4-digit numbers with digit sum equal to 10.

1009, 1018, 1027, 1036, 1045, 1054, 1063, 1072, 1081, 1090, 1108, 1117, 1126, 1135, 1144, 1153, 1162, 1171, 1180, 1207, 1216, 1225, 1234, 1243, 1252, 1261, 1270, 1306, 1315, 1324, 1333, 1342, 1351, 1360, 1405, 1414, 1423, 1432, 1441, 1450, 1504, 1513, 1522, 1531, 1540, 1603, 1612, 1621, 1630, 1702, 1711, 1720, 1801, 1810, 1900, 2008, 2017, 2026, 2035, 2044, 2053, 2062, 2071, 2080, 2107, 2116, 2125, 2134, 2143, 2152, 2161, 2170, 2206, 2215, 2224, 2233, 2242, 2251, 2260, 2305, 2314, 2323, 2332, 2341, 2350, 2404, 2413, 2422, 2431, 2440, 2503, 2512, 2521, 2530, 2602, 2611, 2620, 2701, 2710, 2800, 3007, 3016, 3025, 3034, 3043, 3052, 3061, 3070, 3106, 3115, 3124, 3133, 3142, 3151, 3160, 3205, 3214, 3223, 3232, 3241, 3250, 3304, 3313, 3322, 3331, 3340, 3403, 3412, 3421, 3430, 3502, 3511, 3520, 3601, 3610, 3700, 4006, 4015, 4024, 4033, 4042, 4051, 4060, 4105, 4114, 4123, 4132, 4141, 4150, 4204, 4213, 4222, 4231, 4240, 4303, 4312, 4321, 4330, 4402, 4411, 4420, 4501, 4510, 4600, 5005, 5014, 5023, 5032, 5041, 5050, 5104, 5113, 5122, 5131, 5140, 5203, 5212, 5221, 5230, 5302, 5311, 5320, 5401, 5410, 5500, 6004, 6013, 6022, 6031, 6040, 6103, 6112, 6121, 6130, 6202, 6211, 6220, 6301, 6310, 6400, 7003, 7012, 7021, 7030, 7102, 7111, 7120, 7201, 7210, 7300, 8002, 8011, 8020, 8101, 8110, 8200, 9001, 9010, 9100.
Thank you.

Re: Counting Numbers with a Given Digit Sum

Posted: Wed Sep 08, 2021 3:44 pm
by sakib17442
Can you please show us your mathematical process for this problem or programming source code?

Re: Counting Numbers with a Given Digit Sum

Posted: Sat Sep 11, 2021 2:50 am
by Anindya Biswas
Can't post a thing, please fix this bug. For the problem above, use stars and bars formula.