用32粒围棋子在棋盘上组成一个两层中空方阵，如果在方阵外面再围3层，还需要多少粒棋子？ 小学生奥数：方阵问题
\u6676\u6676\u7528\u56f4\u68cb\u5b50\u6446\u6210\u4e2a\u4e24\u5c42\u7a7a\u5fc3\u65b9\u9635\u6700\u5916\u4e00\u5c42\u6bcf\u8fb9\u6709\u56f4\u68cb\u5b5018\u4e2a\u3002\u6700\u5916\u5c42\u5171\u6709\u56f4\u68cb\u5b50\u591a\u5c11\u4e2a?\u6676\u6676\u6446\u8fd9\u4e2a\u65b9\u9635\u5171\u6700\u5916\u5c42\u5171\u6709:
18\u00d74-4=78
\u65b9\u9635\u7684\u57fa\u672c\u7279\u70b9:
(1)\u65b9\u9635\u4e0d\u8bba\u54ea\u4e00\u5c42,\u6bcf\u8fb9\u4e0a\u7684\u4eba(\u6216\u7269)\u6570\u91cf\u90fd\u76f8\u540c,\u6bcf\u5411\u91cc\u4e00\u5c42,\u6bcf\u8fb9\u4e0a\u7684 \u4eba\u6570\u5c31\u5c112\u3002
(2)\u6bcf\u8fb9\u4eba(\u6216\u7269)\u6570\u548c\u56db\u5468\u4eba(\u6216\u7269)\u7684\u5173\u7cfb;
\u56db\u5468\u4eba(\u6216\u7269)\u6570=[\u6bcf\u8fb9\u4eba(\u6216\u7269)\u6570-1]\u00d74
\u6bcf\u8fb9\u4eba(\u6216\u7269)\u6570=\u56db\u5468\u4eba(\u6216\u7269)\u6570\u00f74+1
(3)\u4e2d\u5b9e\u65b9\u9635\u7684\u603b\u4eba\u6570(\u6216\u7269)=\u6bcf\u8fb9\u4eba(\u6216\u7269)\u6570\u00d7\u6bcf\u8fb9\u4eba(\u6216\u7269)\u6570
(4)\u7a7a\u5fc3\u65b9\u9635\u7684\u603b\u4eba(\u6216\u7269)\u6570=\uff08\u6700\u5916\u5c42\u6bcf\u8fb9\u4eba(\u6216\u7269)\u6570\uff0d\u7a7a\u5fc3\u65b9\u9635\u7684\u5c42\u6570\uff09\u00d7\u7a7a\u5fc3\u65b9\u9635\u7684\u5c42\u6570\u00d74
1\u9898\uff0c\u5957(2),
\u4ee4\u6bcf\u8fb9\u4eba\u6570\u4e3aA,
\u5f97 (A-1)4=84
A=22
(1)\u53ef\u77e5\u5411\u91cc\u4e00\u5c42,\u6bcf\u8fb9\u5c112,\u6240\u4ee5\u9ed1\u8272\u4e3a(22-2)*(22-2)=400\u679a
2\u9898\uff0c\u5957\uff084\uff09
\u5f97 \u603b\u6570=\uff0816-3\uff09x3x4=156
3\u9898\uff0c\u5957\uff084\uff09
\u5f97 \u603b\u6570=\uff0812-4\uff09x4x4=128
4\u9898\uff0c\u5957\uff084\uff09
\u5f97 \u603b\u6570=\uff0813-2\uff09x2x4=88
5\u9898\uff1b\u5957\uff082\uff09
\u4ee4\u6bcf\u8fb9\u4eba\u6570\u4e3aA,
\u5f97 (A-1)4=36
A=10
\u65b9\u9648\u603b\u6570\u4e3a10x10=100
6\u9898\uff0c\u5957 \uff084\uff09
120=\uff08A-2\uff09X2X4
\u6240\u4ee5 A=17
7\u9898\u5957\uff084\uff09
40=\uff08A-2\uff09X2X4
\u6700\u5916\u5c42\uff1aA=7 \u7b2c\u4e8c\u5c42\u4e3a 7-2=5
8\u9898\uff0c\u5957\uff084\uff09 \u8bbe\u6700\u5916\u5c42\u4e3aA\uff0c
64=\uff08A-2\uff09X2X4
A=10
\u589e\u52a0\u6700\u5916\u5c42\u4e3a10+2=12\u4eba\u3002\u5957\uff082\uff09
\u5f97\uff0812-1\uff09x4=44\u4eba
9\u9898\uff0c\u6700\u5185\u5c42\u6bcf\u884c\u4eba\u6570\u4e3aA\uff0c\u5957\uff082\uff09
\uff08A-1\uff09x4=28\u4eba \u5f97\uff1aA=8
\u6700\u5916\u5c42\u6bcf\u884c\u4eba\u6570\u4e3aB\uff0c\u5957\uff082\uff09
\uff08A-1\uff09x4=44\u4eba \u5f97\uff1aB=12
\u6240\u4ee5\u51713\u5c42\uff0c\u5957\uff084\uff09
\u5f97\uff1a \u603b\u6570=\uff0812-3\uff09X3X4=108\u4eba
10\u9898\uff0c\u53ef\u77e5\u9053\uff0c\u589e\u52a0\u7684\u4e00\u5c42\u9700\u898116\u4eba\uff0c
\u5957\uff084\uff09\uff0c\u8bbe\u6b64\u5c42\u6bcf\u8fb9\u4e3aA\u4eba\uff0c
16=\uff08A-4\uff09X4X4
\u5f97A=5
\u6240\u4ee5\u6700\u5916\u5c42\u4eba\u6570\u4e3a5+3x2=11\u4eba
\u603b\u4eba\u6570\u5957\uff084\uff09\u518d\u52a09
\u5f97\uff0c\u603b\u6570=\uff0811-3\uff09x3x4+9=105\u4eba
\u603b\u5171\u82b1\u4e86\u534a\u4e2a\u5c0f\u65f6\u8f93\u8fdb\u53bb\uff0c\u8bf7\u91c7\u7eb3\uff0c\u8c22\u8c22\u3002
最外层6枚，
(6+3)×3×4＝108，
还需要108枚。
外层比内层多8粒
最内层有:（32-8）÷2=12粒
再围三层需要:
12+2×8+12+3×8+12+4×8
=36+16+24+32
=68+40
=108粒
绛旓細32梅4梅2+1脳2锛6锛屾渶澶栧眰6鏋氾紝(6+3)脳3脳4锛108锛岃繕闇瑕108鏋氥
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