从1——999的所有自然数中,不含有数字6的自然数有多少

从1——999的所有自然数中,不含有数字6的自然数有多少

1-100 含6有10个
101-200 含6的有 10+9=19个
201-300...都和101-200的一样
因此有 10+19*9=181（个）
答：不含有数字6的自然数有181个。

看有多少个含6的然后再排除。 总共有999个数 1~100中: 6 16 26 36 46 56 60 61 62 63 64 65 66 67 68 69 76 86 96 19个 同理 百位为0 1 2 3 4 5 7 8 9 的都是。 而百位为6的 则全部含6 600~699 总共100个数。 所以含6的有 19*9+100=271 不含6的 999-271=728

C(8,1)+C(8,1)*C(9,1)+C(8,1)*C(9,1)*C(9,1) =8+8*9+8*9*9=728 含6的数有271个,它们是: 6,16,26,36,46,56,60,61,62,63,64,65,66,67,68,69,76,86,96,106,116,126,136,146,156,160,161,162,163,164,165,166,167,168,169,176,186,196,206,216,226,236,246,256,260,261,262,263,264,265,266,267,268,269,276,286,296,306,316,326,336,346,356,360,361,362,363,364,365,366,367,368,369,376,386,396,406,416,426,436,446,456,460,461,462,463,464,465,466,467,468,469,476,486,496,506,516,526,536,546,556,560,561,562,563,564,565,566,567,568,569,576,586,596,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,6缉触光吠叱杜癸森含缉52,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,706,716,726,736,746,756,760,761,762,763,764,765,766,767,768,769,776,786,796,806,816,826,836,846,856,860,861,862,863,864,865,866,867,868,869,876,886,896,906,916,926,936,946,956,960,961,962,963,964,965,966,967,968,969,976,986,996

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