Counting Numbers with a Given Digit Sum

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Sujoy Mollick
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Counting Numbers with a Given Digit Sum

Unread post by Sujoy Mollick » 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 \(10\)?

103568
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Location:Sylhet

Re: Counting Numbers with a Given Digit Sum

Unread post by 103568 » Wed Aug 18, 2021 10:30 am

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.

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sakib17442
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Re: Counting Numbers with a Given Digit Sum

Unread post by sakib17442 » Wed Sep 08, 2021 3:44 pm

Can you please show us your mathematical process for this problem or programming source code?
Games You can't win because you'll play against yourself.
---Dr.Seuss

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Anindya Biswas
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Re: Counting Numbers with a Given Digit Sum

Unread post by Anindya Biswas » Sat Sep 11, 2021 2:50 am

Can't post a thing, please fix this bug. For the problem above, use stars and bars formula.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

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