Form 1 MATH 問題－ohe09nz81r的部落格

標題:

Form 1 MATH 問題

發問:

From 1 to 1000,how many numbers are there with digits having a sum of 10? 答案寫住:63 我想知WHY~

最佳解答:

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)

其他解答:

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)|||||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.