40．从1到500的所有自然数中，不含有数字4的自然数有多少个？
\u4ece1\u5230500\u7684\u6240\u6709\u81ea\u7136\u6570\u4e2d\uff0c\u4e0d\u542b\u6709\u6570\u5b574\u7684\u81ea\u7136\u6570\u6709\u591a\u5c11\u4e2a\uff1f\uff08 \uff09\u5206\u6790
\u4ece1\u5230500\u7684\u6240\u6709\u81ea\u7136\u6570\u53ef\u5206\u4e3a\u4e09\u5927\u7c7b\uff0c\u5373\u4e00\u4f4d\u6570\uff0c\u4e24\u4f4d\u6570\uff0c\u4e09\u4f4d\u6570\uff0e
\u4e00\u4f4d\u6570\u4e2d\uff0c\u4e0d\u542b4\u7684\u67098\u4e2a\uff0c\u5b83\u4eec\u662f1\u30012\u30013\u30015\u30016\u30017\u30018\u30019\uff1b
\u4e24\u4f4d\u6570\u4e2d\uff0c\u4e0d\u542b4\u7684\u53ef\u4ee5\u8fd9\u6837\u8003\u8651\uff1a\u5341\u4f4d\u4e0a\uff0c\u4e0d\u542b4\u7684\u67091\u30012\u30013\u30015\u30016\u30017\u30018\u30019\u8fd9\u516b\u79cd\u60c5\u51b5\uff0e\u4e2a\u4f4d\u4e0a\uff0c\u4e0d\u542b4\u7684\u67090\u30011\u30012\u30013\u30015\u30016\u30017\u30018\u30019\u8fd9\u4e5d\u79cd\u60c5\u51b5\uff0c\u8981\u786e\u5b9a\u4e00\u4e2a\u4e24\u4f4d\u6570\uff0c\u53ef\u4ee5\u5148\u53d6\u5341\u4f4d\u6570\uff0c\u518d\u53d6\u4e2a\u4f4d\u6570\uff0c\u5e94\u7528\u4e58\u6cd5\u539f\u7406\uff0c\u8fd9\u65f6\u5171\u67098\u00d79=72\u4e2a\u6570\u4e0d\u542b4\uff0e
\u4e09\u4f4d\u6570\u4e2d\uff0c\u5c0f\u4e8e500\u5e76\u4e14\u4e0d\u542b\u6570\u5b574\u7684\u53ef\u4ee5\u8fd9\u6837\u8003\u8651\uff1a\u767e\u4f4d\u4e0a\uff0c\u4e0d\u542b4\u7684\u67091\u30012\u30013\u3001\u8fd9\u4e09\u79cd\u60c5\u51b5\uff0e\u5341\u4f4d\u4e0a\uff0c\u4e0d\u542b4\u7684\u67090\u30011\u30012\u30013\u30015\u30016\u30017\u30018\u30019\u8fd9\u4e5d\u79cd\u60c5\u51b5\uff0c\u4e2a\u4f4d\u4e0a\uff0c\u4e0d\u542b4\u7684\u4e5f\u6709\u4e5d\u79cd\u60c5\u51b5\uff0e\u8981\u786e\u5b9a\u4e00\u4e2a\u4e09\u4f4d\u6570\uff0c\u53ef\u4ee5\u5148\u53d6\u767e\u4f4d\u6570\uff0c\u518d\u53d6\u5341\u4f4d\u6570\uff0c\u6700\u540e\u53d6\u4e2a\u4f4d\u6570\uff0c\u5e94\u7528\u4e58\u6cd5\u539f\u7406\uff0c\u8fd9\u65f6\u5171\u67093\u00d79\u00d79=243\u4e2a\u4e09\u4f4d\u6570\uff0e\u7531\u4e8e500\u4e5f\u662f\u4e00\u4e2a\u4e0d\u542b4\u7684\u4e09\u4f4d\u6570\uff0e\u6240\u4ee5\uff0c1\uff5e500\u4e2d\uff0c\u4e0d\u542b4\u7684\u4e09\u4f4d\u6570\u5171\u67093\u00d79\u00d79+1=244\u4e2a\uff0e
\u89e3\uff1a\u57281\uff5e500\u4e2d\uff0c\u4e0d\u542b4\u7684\u4e00\u4f4d\u6570\u67098\u4e2a\uff1b\u4e0d\u542b4\u7684\u4e24\u4f4d\u6570\u67098\u00d79=72\u4e2a\uff1b\u4e0d\u542b4\u7684\u4e09\u4f4d\u6570\u67093\u00d79\u00d79+1=244\u4e2a\uff0c\u7531\u52a0\u6cd5\u539f\u7406\uff0c\u57281\uff5e500\u4e2d\uff0c\u5171\u6709\uff1a
8+8\u00d79+3\u00d79\u00d79+1=324\uff08\u4e2a\uff09
\u4e0d\u542b4\u7684\u81ea\u7136\u6570\uff0e
\u8865\u5145\u8bf4\u660e\uff1a\u8fd9\u9053\u9898\u4e5f\u53ef\u4ee5\u8fd9\u6837\u60f3\uff1a\u628a\u4e00\u4f4d\u6570\u770b\u6210\u662f\u524d\u9762\u6709\u4e24\u4e2a0\u7684\u4e09\u4f4d\u6570\uff0c\u5982\uff1a\u628a1\u770b\u6210\u662f001\uff0e\u628a\u4e24\u4f4d\u6570\u770b\u6210\u662f\u524d\u9762\u6709\u4e00\u4e2a0\u7684\u4e09\u4f4d\u6570\uff0e\u5982\uff1a\u628a11\u770b\u6210011\uff0e\u90a3\u4e48\u6240\u6709\u7684\u4ece1\u5230500\u7684\u81ea\u7136\u6570\u90fd\u53ef\u4ee5\u770b\u6210\u662f\u201c\u4e09\u4f4d\u6570\u201d\uff0c\u9664\u53bb500\u5916\uff0c\u8003\u8651\u4e0d\u542b\u67094\u7684\u8fd9\u6837\u7684\u201c\u4e09\u4f4d\u6570\u201d\uff0e\u767e\u4f4d\u4e0a\uff0c\u67090\u30011\u30012\u30013\u8fd9\u56db\u79cd\u9009\u6cd5\uff1b\u5341\u4f4d\u4e0a\uff0c\u67090\u30011\u30012\u30013\u30015\u30016\u30017\u30018\u30019\u8fd9\u4e5d\u79cd\u9009\u6cd5\uff1b\u4e2a\u4f4d\u4e0a\uff0c\u4e5f\u6709\u4e5d\u79cd\u9009\u6cd5\uff0e\u6240\u4ee5\uff0c\u9664500\u5916\uff0c\u67094\u00d79\u00d79=324\u4e2a\u4e0d\u542b4\u7684\u201c\u4e09\u4f4d\u6570\u201d\uff0e\u6ce8\u610f\u5230\uff0c\u8fd9\u91cc\u9762\u6709\u4e00\u4e2a\u6570\u662f000\uff0c\u5e94\u8be5\u53bb\u6389\uff0e\u800c500\u8fd8\u6ca1\u6709\u7b97\u8fdb\u53bb\uff0c\u5e94\u8be5\u52a0\u8fdb\u53bb\uff0e\u6240\u4ee5\uff0c\u4ece1\u5230500\u4e2d\uff0c\u4e0d\u542b4\u7684\u81ea\u7136\u6570\u4ecd\u6709324\u4e2a\uff0e
\u628a\u6570\u5b57\u8f6c\u6362\u6210\u5b57\u7b26\u4e32\uff0c\u67e5\u627e\u5b57\u7b26\u4e32\u4e2d\u662f\u5426\u542b\u67094
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace _5
{
class Program
{
static void Main(string[] args)
{
int count = 0;
for (int i = 1; i <= 500; i++)
{
if (i.ToString().IndexOf("4") == -1)
{
count++;
Console.Write(i+" ");
}
}
Console.WriteLine("\n"+count);
}
}
}
324\u4e2a
100~199：81
200~299：81
300~399：81
400~499：0
500：1
81+81+81+81+1=325（个）
所有自然数，百位数可取0.1.2.3.5,十位数可取1.2.3.5...9,个数数也同样
不含有数字4的自然数＝5×8×8＝320个
绛旓細鍒嗘瀽 浠1鍒500鐨勬墍鏈夎嚜鐒舵暟鍙垎涓轰笁澶х被锛鍗充竴浣嶆暟锛屼袱浣嶆暟锛屼笁浣嶆暟锛庝竴浣嶆暟涓紝涓嶅惈4鐨勬湁8涓紝瀹冧滑鏄1銆2銆3銆5銆6銆7銆8銆9锛涗袱浣嶆暟涓紝涓嶅惈4鐨勫彲浠ヨ繖鏍疯冭檻锛氬崄浣嶄笂锛屼笉鍚4鐨勬湁1銆2銆3銆5銆6銆7銆8銆9杩欏叓绉嶆儏鍐碉紟涓綅涓婏紝涓嶅惈4鐨勬湁0銆1銆2銆3銆5銆6銆7銆8銆9杩欎節绉嶆儏鍐...
绛旓細鍒嗘瀽 浠1鍒500鐨勬墍鏈夎嚜鐒舵暟鍙垎涓轰笁澶х被锛鍗充竴浣嶆暟锛屼袱浣嶆暟锛屼笁浣嶆暟锛 涓浣嶆暟涓紝涓嶅惈4鐨勬湁8涓紝瀹冧滑鏄1銆2銆3銆5銆6銆7銆8銆9锛 涓や綅鏁颁腑锛屼笉鍚4鐨勫彲浠ヨ繖鏍疯冭檻锛氬崄浣嶄笂锛屼笉鍚4鐨勬湁1銆2銆3銆5銆6銆7銆8銆9杩欏叓绉嶆儏鍐碉紟涓綅涓婏紝涓嶅惈4鐨勬湁0銆1銆2銆3銆5銆6銆7銆8銆9杩欎節绉...
绛旓細500锛1 81+81+81+81+1=325锛堜釜锛
绛旓細30鍒39鏈9涓紝40鍒49鏈0涓紝50鍒59鏈9涓紝60鍒69鏈9涓紝70鍒79鏈9涓紝80鍒89鏈9涓紝90鍒99鏈9涓紝鍗1鍒99鏈80涓笉鍚湁4鐨勮嚜鐒舵暟锛屽悓鐞100鍒199鏈81涓紝200鍒299鏈81涓紝300鍒399鏈81涓紝400鍒499鏈0,500鏈1涓紝
绛旓細浠1鍒500鐨勮嚜鐒舵暟鍙垎涓轰笁绫伙紝鍗充竴浣嶆暟锛屼袱浣嶆暟锛屼笁浣嶆暟锛庝竴浣嶆暟涓笉鍚暟瀛8鐨勬湁8涓細1銆2銆3銆4銆5銆6銆7銆9锛庝袱浣嶆暟涓笉鍚暟瀛8鐨勬湁锛8脳9=72锛堜釜锛夛紟鍗佷綅鍙湁1銆2銆3銆4銆5銆6銆7銆9杩8绉嶅彇娉曪紱涓綅鏁板瓧鏈0銆1銆2銆3銆4銆5銆6銆7銆9杩9绉嶅彇娉曪紟涓変綅鏁颁腑涓嶅惈鏁板瓧8鐨勬湁锛4...
绛旓細瑙ｏ細璁浠1鍒500鐨勬墍鏈夎嚜鐒舵暟涓,鏈墄涓暟涔樹互24鍚庢槸瀹屽叏骞虫柟鏁 24=2*2*2*3 6*x^2<=500 x^2<86.7 x<=9 绛旓細浠1鍒500鐨勬墍鏈夎嚜鐒舵暟涓,鏈9涓暟涔樹互24鍚庢槸瀹屽叏骞虫柟鏁 ---鍒椾妇:6銆24銆54銆96銆150銆216銆294銆384銆486
绛旓細9+9*9+4*9*9 =9+5*81 =9+405 =414 鍦1鍒500鐨勮嚜鐒舵暟,涓嶅惈鏁板瓧0鐨勬暟鍏辨湁414涓 --- 涓浣嶆暟9涓 浜屼綅鏁9*9=81涓 涓変綅鏁4*9*9=324涓
绛旓細銆愮瓟妗堛戯細B 鎶婁竴浣嶆暟鐪嬫垚鏄墠闈㈡湁涓や釜0鐨勪笁浣嶆暟:濡傦細鎶1鐪嬫垚鏄001;鎶婁袱浣嶆暟鐪嬫垚鏄墠闈㈡湁涓涓0鐨勪笁浣嶆暟:濡傦細鎶11鐪嬫垚011;閭ｄ箞鎵鏈夌殑浠1鍒500鐨勮嚜鐒舵暟閮藉彲浠ョ湅鎴愭槸鈥滀笁浣嶆暟鈥濄傞櫎鍘500澶栵紝鑰冭檻涓嶅惈鏈4鐨勮繖鏍风殑鈥滀笁浣嶆暟鈥濓細鐧句綅涓婏紝鏈0銆1銆2銆3杩欏洓绉嶉夋硶;鍗佷綅涓婏紝鏈0銆1銆2銆3銆5銆...
绛旓細浠1鍒500鐨勬墍鏈夎嚜鐒舵暟涓紝涓嶅惈鏈夋暟瀛4鐨勮嚜鐒舵暟鏈324涓紝1鈥99涓湁80涓紝鐧句綅鏄1鐨勬湁81涓紝鍚岀悊锛岀櫨浣嶆槸2銆3鐨勫垎鍒篃鏈81涓紝鐧句綅鏄5鐨勬湁1涓紝鍏辫锛80+81+81+81+1=324锛堜釜锛夊笇鏈涜兘甯埌浣狅紒
绛旓細1鍒10鏈1涓湁4锛11鍒20鏈1涓湁4锛屽嵆閫10鏈1涓紝鏁呭甫4鐨勬暟瀛楀湪500浠ュ唴鍏辨湁500/10=50涓紝鎵浠ヤ笉甯4鐨勬暟瀛楁湁500-50=450涓
