数阵分析
\u7814\u7a76\u6570\u9635\u8fd9\u662f\u6768\u8f89\u4e09\u89d2
http://baike.baidu.com/view/7804.htm?fr=ala0_1_1
\u4f60\u53ef\u4ee5\u53bb\u767e\u5ea6\u767e\u79d1\u8be6\u7ec6\u770b\u4e00\u4e0b
1 9 36 84 126 126 84 36 9 1
\u548c512
\u9996\u5148\uff0c\u7ea0\u6b63\u4e00\u4e0b\u697c\u4e3b\u7684\u9898\u76ee\uff0c\u6570\u9635\u4e2d\u7684\uff083\uff0c3\uff09\u5e94\u8be5\u4e3a13
\u5f00\u59cb\u89e3\u9898\uff1a
\u7531\u8868\u53ef\u5f97\u6a2a\u6392\u6570\u5217\u7684\u89c4\u5f8b\u662f\uff08n\uff0c1\uff09=n+[(n-1)(n-2)/2]
\u6240\u4ee5\uff08100\uff0c1\uff09\u6240\u8868\u793a\u7684\u6570\u662f\uff08 4951\uff09\uff1b\uff08n\uff0c1\uff09\u6240\u8868\u793a\u7684\u6570\u662f
\uff08n+[(n-1)(n-2)/2] \uff09
\u7531\u8868\u53ef\u5f97\u7ad6\u6392\u6570\u5217\u7684\u89c4\u5f8b\u662f\uff081\uff0cn\uff09=n+[n(n-1)/2]
\u800c\uff08m,n\uff09=(m+1)*(n-1)+(n-1)(n-2)/2+m+[(m-1)(m-2)/2]
\u6240\u4ee5\uff081\uff0c20\uff09\u6240\u8868\u793a\u7684\u6570\u662f\uff08210\uff09\uff0c \uff084\uff0c20\uff09\u6240\u8868\u793a\u7684\u6570\u662f\uff08273 \uff09\u3002
(5,5)\u6240\u8868\u793a\u7684\u6570\u4e3a\uff0841\uff09\uff0c\uff08100\uff0c100\uff09\u6240\u8868\u793a\u7684\u6570\u4e3a\uff0819801\uff09
\u5230\u8fd9\u8fb9\u4e3a\u6b62\uff0c\u4ee5\u4e0a\u7684\u8fd9\u79cd\u89e3\u6cd5\u90fd\u80fd\u89e3\u51b3\u95ee\u9898\uff0c\u4f46\u662f\u63a5\u4e0b\u53bb\u6c422008\u5982\u4f55\u8868\u793a\u5c31\u9ebb\u70e6\u4e86\uff0c\u4e8e\u662f\u5f15\u5165\u53e6\u4e00\u79cd\u89e3\u6cd5\uff1a
\u9996\u5148\u89c2\u5bdf\u6570\u9635\uff0c\u53ef\u4ee5\u53d1\u73b0\u4ece\u6a2a\u6392\u7b2c\u4e00\u6392\u7684\u4efb\u610f\u6570\u5b57\u5f00\u59cb\u5f80\u5de6\u4e0b\u89d245\u5ea6\u6210\u5bf9\u89d2\u7ebf\u7684\u4e00\u4e32\u6570\u5217\u90fd\u662f\u76f8\u8fde\u7684\u81ea\u7136\u6570\uff0c\u5e76\u4e14\u662f\u9010\u6e10\u9012\u589e\uff0c\u5982\uff083\uff0c1\uff09\u76844\uff0c\u5f80\u5de6\u4e0b\u89d245\u5ea6\u6210\u5bf9\u89d2\u7ebf\u7684\u4e00\u4e32\u6570\u5217\u5206\u522b\u662f\uff082\uff0c2\uff09\u76845\u3001\uff081\uff0c3\uff09\u76846\uff0c\u5e76\u4e14\u8fd9\u6761\u5bf9\u89d2\u7ebf\u4e0a\u7684\u4e00\u4e32\u6570\u5b57\u7684\u6a2a\u7eb5\u5750\u6807\u76f8\u52a0\u6240\u5f97\u7684\u548c\u76f8\u7b49\uff0c\u5982\uff083\uff0c1\uff09\u3001\uff082\uff0c2\uff09\u3001\uff081\uff0c3\uff09\uff0c\u91cc\u9762\u6a2a\u7eb5\u5750\u6807\u76f8\u52a0\u90fd\u4e3a4\u3002
\u6839\u636e\u8fd9\u4e2a\u65b9\u6cd5\u4e5f\u53ef\u4ee5\u7b80\u5355\u7684\u63a8\u7b97\u51fa\u4e0a\u9762\u90a3\u4e9b\uff084\uff0c20\uff09\u3001\uff085\uff0c5\uff09\u3001\uff08100\uff0c100\uff09\u7b49\u5750\u6807\u6240\u8868\u793a\u7684\u6570\u3002
\u4ee5\uff084\uff0c20\uff09\u4e3a\u4f8b\u3002\u7531\u4e8e\uff084\uff0c20\uff09\u5176\u6a2a\u7eb5\u5750\u6807\u76f8\u52a0\u4e3a4+20=24\uff0c\u56e0\u6b64\u8fd9\u4e2a\u5750\u6807\u6240\u8868\u793a\u7684\u6570\u5b57\u5728\uff0823\uff0c1\uff09\u4e0e\uff081\uff0c23\uff09\u76f8\u8fde\u7684\u5bf9\u89d2\u659c\u7ebf\u4e0a\u3002\u7531\u4e8e
\u7ad6\u6392\u6570\u5217\u7684\u89c4\u5f8b\u662f\uff081\uff0cn\uff09=n+[n(n-1)/2]\uff0c\u6240\u4ee5\u7b80\u5355\u53ef\u7b97\u5f97\uff081\uff0c23\uff09\u4e0a\u7684\u6570\u5b57\u4e3a276\uff0c\u800c\uff081\uff0c23\uff09\u4e3a\u5bf9\u89d2\u659c\u7ebf\u4e0a\u6700\u4e0b\u9762\u7684\u4e00\u4e2a\u70b9\u6240\u4ee5\uff081\uff0c23\uff09\u4e5f\u662f\u8be5\u659c\u7ebf\u4e0a\u6700\u5927\u7684\u6570\uff0c\u659c\u7ebf\u4e0a\u7531\uff081\uff0c23\uff09\u8fd9\u4e2a\u70b9\u5f80\u4e0a\u4f9d\u6b21\u9012\u51cf\uff0c\u5e76\u4e14\u76f8\u90bb\u4e24\u4e2a\u70b9\u6240\u8868\u793a\u7684\u6570\u4e4b\u95f4\u7684\u5dee\u90fd\u4e3a1\uff0c\u6240\u4ee5\uff082\uff0c22\uff09\u4e3a275\u3001\uff083\uff0c21\uff09\u4e3a274\u3001\uff084\uff0c20\uff09\u4e3a273\u2026\u2026\uff0823\uff0c1\uff09\u4e3a254\u3002\u800c\u5176\u4e2d\uff084\uff0c20\uff09\u4e0e\uff081\uff0c23\uff09\u76f8\u5dee23-20=3\u4e2a\u4f4d\u7f6e\uff0c\u6240\u4ee5\uff084\uff0c20\uff09=276-3=273
\u540c\u6837\uff0c\u8ba1\u7b97\uff085\uff0c5\uff09\u65f6\uff0c\u7531\u4e8e\uff085\uff0c5\uff09\u5728\uff089\uff0c1\uff09\u4e0e\uff081\uff0c9\uff09\u4e4b\u95f4\u7684\u5bf9\u89d2\u659c\u7ebf\u4e0a\uff0c\u6240\u4ee5\u7b97\u5f97\uff081\uff0c9\uff09=45\uff0c\u800c\uff085\uff0c5\uff09\u4e0e\uff081\uff0c9\uff09\u76f8\u5dee9-5=4\u4e2a\u4f4d\u7f6e\uff0c\u6240\u4ee5\uff085\uff0c5\uff09=45-4=41
\u540c\u6837\uff0c\u8ba1\u7b97\uff08100\uff0c100\uff09\u65f6\uff0c\u7531\u4e8e\uff08100\uff0c100\uff09\u5728\uff08199\uff0c1\uff09\u4e0e\uff081\uff0c199\uff09\u4e4b\u95f4\u7684\u5bf9\u89d2\u659c\u7ebf\u4e0a\uff0c\u6240\u4ee5\u7b97\u5f97\uff081\uff0c199\uff09=19900\uff0c\u800c\uff08100\uff0c100\uff09\u4e0e\uff081\uff0c199\uff09\u4e4b\u95f4\u76f8\u5dee199-100=99\u4e2a\u4f4d\u7f6e\uff0c\u6240\u4ee5\uff08100\uff0c100\uff09=19900-99=19801
\u63a5\u4e0b\u6765\u662f\u89e3\u51b32008\u6240\u5728\u7684\u5750\u6807\u95ee\u9898\u3002
\u7531\u4e8e\u5148\u524d\u5206\u6790\u8fc7\uff0c\u6bcf\u676145\u5ea6\u5bf9\u89d2\u659c\u7ebf\u4e2d\u7684\u6570\u5217\uff0c\u6a2a\u884c\u7b2c\u4e00\u884c\u7684\u90a3\u4e2a\u6570\u662f\u6574\u4e2a\u6570\u5217\u6700\u5c0f\u7684\uff0c\u800c\u7ad6\u6392\u7b2c\u4e00\u6392\u7684\u90a3\u4e2a\u6570\uff08\u5373\u6a2a\u884c\u6700\u540e\u4e00\u884c\u7684\u90a3\u4e2a\u6570\uff09\u662f\u6574\u4e2a\u6570\u5217\u6700\u5927\u7684\u3002\u6240\u4ee52008\u5fc5\u7136\u4e5f\u843d\u5728\u8fd9\u79cd45\u5ea6\u5bf9\u89d2\u659c\u7ebf\u7684\u6570\u5217\u4e2d\u3002\uff08\u89c2\u5bdf\u6570\u5217\u53ef\u4ee5\u770b\u5230\uff0c\u7b2c\u4e00\u659c\u5217\u4e3a1\uff0c\u7b2c\u4e8c\u659c\u5217\u4e3a2\u30013\uff0c\u7b2c\u4e09\u659c\u5217\u4e3a4\u30015\u30016\u2026\u2026\u6240\u6709\u81ea\u7136\u6570\u6309\u987a\u5e8f\u5206\u5e03\u5728\u8fd9\u4e9b\u659c\u5217\u4e2d\uff0c\u6240\u4ee52008\u4e5f\u5fc5\u7136\u5728\u67d0\u4e2a\u659c\u5217\u4e2d\uff09\u3002\u5982\u4eca\u6211\u4eec\u8981\u627e\u51fa2008\u6240\u5728\u659c\u5217\u7684\u5934\u5c3e\u4e24\u4e2a\u70b9\u3002
\u5047\u8bbe2008\u5728\uff08n,1\uff09\u4e0e\uff081\uff0cn\uff09\u4e4b\u95f4\u7684\u659c\u7ebf\u6240\u7ec4\u6210\u7684\u659c\u5217\u4e2d\uff0c\u90a3\u4e48\u7531\u4e8e\u7ad6\u6392\u6570\u5217\u7684\u89c4\u5f8b\u662f\uff081\uff0cn\uff09=n+[n(n-1)/2]\uff0c\u6240\u4ee5\uff081\uff0cn\uff09=n+[n(n-1)/2]\u300b2008\uff0c\u56e0\u4e3a\uff081\uff0cn\uff09\u662f\u8be5\u659c\u5217\u4e2d\u6700\u5927\u7684\u6570\u3002
\u6240\u4ee5\u53ef\u89e3\u5f97n\u6b64\u65f6\u7684\u6700\u5c0f\u503c\u4e3a63\uff0c\u6240\u4ee52008\u5728\uff0863\uff0c1\uff09\u4e0e\uff081\uff0c63\uff09\u4e4b\u95f4\u7684\u659c\u7ebf\u6240\u7ec4\u6210\u7684\u659c\u5217\u4e2d\u3002\u800c\uff081\uff0c63\uff09=2016\uff0c\u800c2016-2008=8\uff0c\u6240\u4ee52008\u7684\u5750\u6807\u4e0e\uff081\uff0c63\uff09\u76f8\u5dee8\u4e2a\u4f4d\u7f6e\uff0c\u6240\u4ee52008\u7684\u7eb5\u5750\u6807\u4e3a63-8=55\uff0c\u800c\u5176\u6a2a\u5750\u6807\u4e3a63+1-55=9\uff0c\uff08\u56e0\u4e3a\u8be5\u659c\u5217\u4e0a\u6bcf\u4e2a\u5750\u6807\u7684\u6a2a\u7eb5\u5750\u6807\u76f8\u52a0\u90fd\u4e3a63+1=64\uff0c\u90fd\u4e3a64\uff0c\u6240\u4ee5\u5f97\u51fa2008\u7eb5\u5750\u6807\u4e3a55\u540e\uff0c\u81ea\u7136\u753164-55=9\u7b97\u51fa\u5176\u6a2a\u5750\u6807\uff09\u3002
\u56e0\u6b64\uff0c2008\u5e94\u8bb0\u4f5c\uff089\uff0c55\uff09\u3002
4 8
6 12 2
完成！
我直接告诉你我的思路吧，答案的思路也是人想出来的，
只要能解出题目来，自己的方法反而更好！
1、假定顶端放一个数(暂时未知)，那么，左右两条边上，另外两个数之和必然要相等。根据这个，很快且最先想到的是6+4=8+2，那么先就填上这4个数，
接下来，只剩下10和12，我先把10填到顶端，剩下12到底边中端，协调一下，得到了我给出的答案。
当然，将12放到顶端的话，调整下，也可得到：
---------12
6 2
4 10 8
我给你说起来感觉很慢，但是在纸上随便一画就能出来答案！
有时候答案还更费解呢，不是吗？
就比如 8
6 2
4 10 12 符合答案吧？ 但是这就错了！
绛旓細鎴戜滑浠庢荤殑鏍煎眬鍑哄彂锛鍒嗘瀽姣忎釜鏁板瓧鐨勪綔鐢ㄣ'涓'鐢变笁琛屽洓鍒楀拰涓よ涓鍒楃粍鎴愶紝'涓'鍒欏彧鏈変袱琛屻傝繖鎰忓懗鐫鎴戜滑闇瑕佹壘鍒版弧瓒充互涓嬫潯浠剁殑绛夊紡:3涓暟鐩稿姞绛変簬134涓暟鐩稿姞绛変簬132涓暟鐩稿姞绛変簬13鎺ヤ笅鏉ワ紝鎴戜滑閫愪釜鍒楀嚭杩欎簺绛夊紡锛屼互1鍒9涓烘暟瀛楋紝杩涜缁勫悎:3鏁扮浉鍔狅細1+9+3, 1+8+4, 1+7+5, 绛夌瓑2鏁扮浉鍔狅細4...
绛旓細绗竷姝ワ細缁冧範鍜屾彁楂樸傜粍鍚鏁伴樀鍥剧殑瑙ｉ鎶宸ч渶瑕侀氳繃涓嶆柇鐨勭粌涔犳潵鎻愰珮銆傚彲浠ラ氳繃瑙ｅ喅涓嶅悓绫诲瀷鐨勬暟闃靛浘锛屾荤粨瑙ｉ瑙勫緥鍜屾柟娉曘傛讳箣锛岀粍鍚堟暟闃靛浘鏄竴绉嶆湁瓒ｇ殑鏁板娓告垙锛屽畠瑕佹眰鐜╁鍦ㄤ竴涓粰瀹氱殑鍥惧舰涓～鍏ユ暟瀛楋紝浣垮緱姣忔潯杈逛笂鐨勬暟瀛椾箣鍜岄兘鐩哥瓑銆傝В鍐宠繖绫婚棶棰樼殑鍏抽敭鏄悊瑙ｉ鎰忋鍒嗘瀽鍥惧舰銆佸缓绔嬬瓑寮忋佹壘鍑哄叧閿暟瀛...
绛旓細鍒嗘瀽濡備笅锛氬亣璁炬瘡涓笁瑙掑舰鐨勪笁涓暟鐨勫拰涓簁 杩欒竟涓婁笁涓笁瑙掑舰鐨勫拰涓3k 鏈3k+A锛0+1+2+...+8+9锛45 鏈夊洓绉嶆儏鍐 褰揂锛0锛宬锛15锛屼絾15鍙兘鎷嗘垚涓ょ鎯呭喌锛15锛6+9+0锛7+8+0锛屾墍浠ヤ笉婊¤冻 褰揂锛3锛宬锛14锛14-3锛11鍙互鎷嗘垚锛11锛5+6锛4+7锛3+8锛2+9锛屾帓闄3+8锛屾牴鎹绉版э紝鍏...
绛旓細4 8 6 12 2 瀹屾垚锛佹垜鐩存帴鍛婅瘔浣犳垜鐨勬濊矾鍚э紝绛旀鐨勬濊矾涔熸槸浜烘兂鍑烘潵鐨勶紝鍙鑳借В鍑洪鐩潵锛岃嚜宸辩殑鏂规硶鍙嶈屾洿濂斤紒1銆佸亣瀹氶《绔斁涓涓暟(鏆傛椂鏈煡)锛岄偅涔堬紝宸﹀彸涓ゆ潯杈逛笂锛屽彟澶栦袱涓暟涔嬪拰蹇呯劧瑕佺浉绛夈傛牴鎹繖涓紝寰堝揩涓旀渶鍏堟兂鍒扮殑鏄6+4=8+2锛岄偅涔堝厛灏卞～涓婅繖4涓暟锛屾帴涓嬫潵锛屽彧鍓╀笅10鍜12...
绛旓細1.鍒嗘瀽锛氭妸涓や釜鍦堢殑鎵鏈夋暟閮藉姞璧锋潵涔嬪拰鑲畾鏄40锛堝洜涓轰竴涓湀鐨勬墍鏈夋暟涔嬪拰鏄20锛夋樉鐒惰繖绉嶅姞娉曠殑缁撴灉鏄紙1鍒8鎵鏈夌殑鏁颁箣鍜岋級+锛1鍒8涓煇涓や釜鏁扮殑鍜岋級杩欐煇涓や釜鏁板氨鏄腑闂翠袱涓暟锛屽洜涓烘妸瀹冧滑鍔犱簡涓ゆ 鑰岋紝1鍒8鎵鏈夌殑鏁颁箣鍜=36锛屾墍浠ュ氨鏈 1鍒8涓煇涓や釜鏁扮殑鍜岋紙涔熷氨鏄腑闂翠袱涓暟涔嬪拰锛=40...
绛旓細杩欐槸涓涓瘮杈冩湁瓒ｇ殑鏁板瓧娓告垙锛岄渶瑕佷竴浜鍒嗘瀽鍜屽皾璇曟墠鑳芥眰瑙ｃ傞鍏堬紝鎴戜滑鍙互璁炬瘡涓ぇ鍦嗗湀涓婄殑鏁板瓧鍜屼负 S锛屽垯鏍规嵁棰樻剰鍙互鍒楀嚭涓嬪垪鏂圭▼锛歋 = 1 + a + b + c + d S = a + e + f + g + b S = c + g + h + i + d S = e + 2S/5 + f + h 鍏朵腑锛宎 ~ i 琛ㄧず姣忎釜鍦嗗湀涓...
绛旓細銆鍒嗘瀽銆 鍏堟眰1銆2銆3銆4銆5鐨勫拰鏄1+2+3+4+5=15锛屽浘涓腑闂村～鐨勬暟璁＄畻浜嗕袱娆★紝鍋囪鏄疉锛屽垯15+A鐨勫拰闄や互2搴旇娌℃湁浣欐暟锛屾墍浠=1锛3锛5銆 妯銆佺旱琛3涓暟鐨勫拰鍒嗗埆鏄 (1)(15+1)梅2=8锛 (2)(15+3)梅2=9锛 (3)(15+5)梅2=10銆 涓棿鏁颁互澶栫殑鍙︿袱涓暟锛 (1)8-1...
绛旓細鍥犱负杩欎釜鏁伴樀鍙互寰涓嬪欢缁棤闄愯锛屾墍浠ヤ笉鑳芥鍦ㄥ崄瀛楁涓棿鐨勫彧鏈夋暟闃1)鏈宸﹁竟涓鍒,2)鏈鍙宠竟涓鍒,3)鏈涓婇潰涓琛岋紱涓鐪肩湅鍑烘暟闃垫渶涓婇潰涓琛屾渶澶у间负11锛屾墍浠ヤ笉鑰冭檻锛1)鐢卞墠杩鍒嗘瀽寰楋紝鏈宸﹁竟涓鍒楃敱涓婅嚦涓嬬a椤逛负1+12(a-1)=12a-11(a鈮1涓鸿嚜鐒舵暟)2)鍚屼笂杩伴亾鐞嗘槗寰楋紝鏈鍙宠竟涓鍒楃敱涓婅嚦涓嬬b椤逛负...
绛旓細11+锛6+7+8+9+10+11+12+13+14)=101 (2)瑙勫緥濡備笅锛欰 姣忚鏁板瓧鍛堣嚜鐒舵暟杩炵画澧為暱锛屽苟涓旀瘡琛岄2涓釜鏁板瓧涔嬪樊鍗充负琛屾暟 B 鏈夎寰嬪緱鐭ユ瘡琛岀殑绗竴涓暟瀛椾负涓婅鐨勭浜屼釜鏁板瓧+1 鎵浠ユ湁锛氱浜旇鐨勭涓涓暟瀛楁槸15锛岀浉缁ф暟瀛椾负锛15+5锛15+6锛15+7锛15+8銆傘傘傜敱姝ゅ彲寰楋細15+锛5+6+7+8+9+...
绛旓細姹傜殑绗50琛岀殑鏈鍚庝竴涓暟鏄細涓夎褰鏁伴樀涓1锛3锛6锛10锛15锛屸﹁繖鍒楁暟鐨勭50涓暟锛1锛3锛6锛10锛15锛屸︿腑锛1=[1/2]脳1脳锛1+1锛3=[1/2]脳2脳锛2+1锛6=[1/2]脳3脳锛3+1锛10=[1/2]脳4脳锛4+1锛15=[1/2]脳5脳锛5+1锛夆︾敱姝ゅ彲寰楀埌绗琻涓暟琛ㄧず涓猴細[1/2]n锛坣+1锛...
