From 1 to 1000,how many numbers are there with digits having a sum of 10?
答案寫住:63
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Form 1 MATH 問題
2010-09-05 10:29 pm
回答 (3)
2010-09-05 10:46 pm
✔ 最佳答案
1 to 9 : None 10 to 99 :19 , 28 , 37 , 46 , 55 , 64 , 73 , 82 , 91.9 numbers with digits having a sum of 10.100 to 1000 :109 , 118 , 127 , 136 , 145 , 154 , 163 , 172 , 181 , 190 208 , 217 , 226 , 235 , 244 , 253 , 262 , 271 , 280
307 , 316 , 325 , 334 , 343 , 352 , 361 , 370
406 , ........................................ 460
505 , 514 , ........................ 550
604 , ........................640
703 ,.................730
802 , 811 , 820
901 , 91010 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2
= 9(10 + 2)/2 = 54 numbers with digits having a sum of 10.Total 9 + 54 = 63 numbers with digits having a sum of 10.
2010-09-05 14:50:15 補充：
109 , 118 , 127 , 136 , 145 , 154 , 163 , 172 , 181 , 190 (10 numbers)
208 , 217 , 226 , 235 , 244 , 253 , 262 , 271 , 280 (9 numbers)
307 , 316 , 325 , 334 , 343 , 352 , 361 , 370 (8 numbers)
406 , ........................................ 460 (7 numbers)
2010-09-05 14:50:19 補充：
505 , ....... ........................ 550 (6 numbers)
604 , ........................640 (5 numbers)
703 ,.................730 (4 numbers)
802 , 811 , 820 (3 numbers)
901 , 910 (2 numbers)
2010-09-06 12:26 am
1 to 9 : None
10 to 99 :
19 , 28 , 37 , 46 , 55 , 64 , 73 , 82 , 91.
9 numbers with digits having a sum of 10.
100 to 1000 :
109 , 118 , 127 , 136 , 145 , 154 , 163 , 172 , 181 , 190
208 , 217 , 226 , 235 , 244 , 253 , 262 , 271 , 280
307 , 316 , 325 , 334 , 343 , 352 , 361 , 370
406 , ........................................ 460
505 , 514 , ........................ 550
604 , ........................640
703 ,.................730
802 , 811 , 820
901 , 910
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2
= 9(10 + 2)/2 = 54 numbers with digits having a sum of 10.
Total 9 + 54 = 63 numbers with digits having a sum of 10.
109 , 118 , 127 , 136 , 145 , 154 , 163 , 172 , 181 , 190 (10 numbers)
208 , 217 , 226 , 235 , 244 , 253 , 262 , 271 , 280 (9 numbers)
307 , 316 , 325 , 334 , 343 , 352 , 361 , 370 (8 numbers)
406 , ........................................ 460 (7 numbers)
505 , ....... ........................ 550 (6 numbers)
604 , ........................640 (5 numbers)
703 ,.................730 (4 numbers)
802 , 811 , 820 (3 numbers)
901 , 910 (2 numbers)
10 to 99 :
19 , 28 , 37 , 46 , 55 , 64 , 73 , 82 , 91.
9 numbers with digits having a sum of 10.
100 to 1000 :
109 , 118 , 127 , 136 , 145 , 154 , 163 , 172 , 181 , 190
208 , 217 , 226 , 235 , 244 , 253 , 262 , 271 , 280
307 , 316 , 325 , 334 , 343 , 352 , 361 , 370
406 , ........................................ 460
505 , 514 , ........................ 550
604 , ........................640
703 ,.................730
802 , 811 , 820
901 , 910
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2
= 9(10 + 2)/2 = 54 numbers with digits having a sum of 10.
Total 9 + 54 = 63 numbers with digits having a sum of 10.
109 , 118 , 127 , 136 , 145 , 154 , 163 , 172 , 181 , 190 (10 numbers)
208 , 217 , 226 , 235 , 244 , 253 , 262 , 271 , 280 (9 numbers)
307 , 316 , 325 , 334 , 343 , 352 , 361 , 370 (8 numbers)
406 , ........................................ 460 (7 numbers)
505 , ....... ........................ 550 (6 numbers)
604 , ........................640 (5 numbers)
703 ,.................730 (4 numbers)
802 , 811 , 820 (3 numbers)
901 , 910 (2 numbers)
2010-09-05 10:39 pm
如果是兩位數ab，那麼
a+b=10
有x組解
如果是三位數abc，那麼
a+b+c=10
有y組解
最後把x和y相加，得到63.
a+b=10
有x組解
如果是三位數abc，那麼
a+b+c=10
有y組解
最後把x和y相加，得到63.
收錄日期: 2021-04-13 17:29:57
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https://hk.answers.yahoo.com/question/index?qid=20100905000051KK00731