已知1+2+3+…+n的和的个位数字是3，十位数字是0，百位数字不是0，求n最小值．
设1+2+3+…+n=100a+10b+c，
由题意可知：b=0，c=3，
即1+2+3+…+n=100a+3，
∵1+2+3+…+n=
，n(n+1) 2
∴
=100a+3，n(n+1) 2
∴n（n+1）=200a+6，
∵两个连续的自然数相乘，个位数为6的只有自然数的个位是2和3或7和8．
∴n的个位数可能是2，7，
当n=12时，
=78（不合题意，舍去），n(n+1) 2
当n=17时，
=153（不合题意，舍去），n(n+1) 2
当n=22时，
=253（不合题意，舍去），n(n+1) 2
当n=27时，
=378（不合题意，舍去），n(n+1) 2
当n=32时，
=528（不合题意，舍去），n(n+1) 2
当n=37时，
=703（不合题意，舍去）．n(n+1) 2
∴n最小的值是37．
| 完形填空。 | ||||
| I was on a bus one March evening. The driver didn't 1 to start the bus soon because it was not yet 2 . A middle-aged woman got on. Tired and sad, she told her story 3 , not to anyone in particular. On her way to the station, half of her money was stolen. The other half was hidden under her blouse, so she 4 still had some left. A few minutes later, she stopped crying, but still looked unhappy. When all the seats were taken, the driver started the engine. The conductor began to collect fares (车费). When she came to an old man in worn-out clothes, he 5 that he had spent all his money when he had accidentally got on a wrong bus and now he was trying to go home. On hearing this, she ordered the old man to get off the bus. The old man was almost in tears as he 6 her to let him take the bus home. The driver took the conductor's side and repeated the conductor's command (命令,要求). The woman was watching the incident. 7 the driver and the conductor raised their voices at the old man, she interfered (干预). "Stop 8 him! Can't you see he's only trying to get home?" " He doesn't have any money!" the driver shouted. "Well, that's no 9 to throw him off the bus," she insisted. Then she reached inside her blouse, took out her 10 money, and handed in to the conductor." Here's his fare and mine. Just stop giving him a 11 time." All heads turned to the woman. "It's only money," she shrugged. She rode the rest of the way home 12 a happy smile, with the money she'd lost earlier 13 . On the road of life, the help of strangers can 14 our loads and lift our spirits. How much sweeter the 15 will be when we make it a little smoother for others! | ||||
|