这几天我有点烦-珍珠湾ART - Powered by Discuz! Archiver

xyh 发表于 2010-1-7 08:11:14

这几天我有点烦

<br /="/"/><div>这几天我有点烦，绞尽脑汁弄了点题目，结果却很快被这里的高手解决了。看来俺还要继续努力。下面是一道天平称球的问题，看看有多少人能解决。</div><div> </div><div>首先预热一下，来一道经典老题，没有做过的朋友可以做做看，做过的朋友可以温习一下。</div><div> </div><div><strong>第一题：</strong><span style="display:none;">www.ddhw.com</span></div><div>12只球，外形大小完全相同，但是12只球的重量有可能一样，也有可能其中有一只（坏球）偏重，也可能偏轻。</div><div>现在你用一台天平，找出这只坏球并告诉我它偏轻还是偏重，或者告诉我说它跟其余的12只球重量一样。</div><div> </div><div>请问，至少称多少次可以保证告诉我上面的结果？</div><div> </div><div> </div><div><strong>第二题：</strong></div><div><div>14只球，外形大小完全相同，前13只球的重量有可能一样，也有可能其中有一只（坏球）偏重，也可能偏轻。第14只球重量跟前面的12只好球一样。也就是说，你事先能确定某一只球是好球。</div><div> </div><div>现在你用一台天平，找出那只坏球并告诉我它偏轻还是偏重，或者告诉我说跟其余的13只球重量一样。</div><div> </div><div>请问，至少称多少次可以保证告诉我上面的结果？</div></div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div>

TRYIL 发表于 2010-1-7 09:06:58

回复：这几天我有点烦

<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>在无砝码天平上,三次称重结论如下: <br /="/"/>A.选出次品，并确定其轻重,可选12个球; <br /="/"/>B.仅选出次品，并不需知其轻重,可选13个球; <br /="/"/>C.另有一个标准球,仅选出次品，可选14个球; <br /="/"/><br /="/"/><br /="/"/></div><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>

冷饭发表于 2010-1-7 22:47:19

回复：这几天我有点烦

GiveItATry 发表于 2010-1-9 23:27:03

回复：这几天我有点烦

<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div><strong>第一题：</strong></div><div><div>12只球，外形大小完全相同，但是12只球的重量有可能一样，也有可能其中有一只（坏球）偏重，也可能偏轻。</div><div>现在你用一台天平，找出这只坏球并告诉我它偏轻还是偏重，或者告诉我说它跟其余的12只球重量一样。</div><div>请问，至少称多少次可以保证告诉我上面的结果？ <font color="#0000ff">A:3次</font></div><div><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><font size="3"><span style="mso-fareast-font-family: 'Arial Unicode MS'"><font face="Times New Roman">Set 12</font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">只球 = A1A2A3A4B1B2B3B4C1C2C3C4; and A1234=A1A2A3A4, same as B1234,and C1234</span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3">weigh 1) A1234 ~ B1234, if 1)=, weigh 2) C12 ~ C34, if 2) =, then 坏球跟其余的球重量一样----Answer</font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><font size="3"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><span style="mso-spacerun: yes"> </span>if 2) >, then weigh 3) C13 ~ A1C2, if 3) =, C4是坏球偏轻---Answer</span><span style="mso-fareast-font-family: 'Arial Unicode MS'"></span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><font size="3"><span style="mso-fareast-font-family: 'Arial Unicode MS'"><font face="Times New Roman"><span style="mso-spacerun: yes"> </span><span style="mso-spacerun: yes"> </span>if 3) >, </font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">C1是坏球偏重---Answer</span><span style="mso-fareast-font-family: 'Arial Unicode MS'"></span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><font size="3"><span style="mso-fareast-font-family: 'Arial Unicode MS'"><font face="Times New Roman"><span style="mso-spacerun: yes"> </span>if 3) <, C3</font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">是坏球偏轻---Answer</span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span></font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span>if 1) >, weigh 2) A123B1 ~ C123A4, if 2) =, weigh 3) B2 ~ B3, if 3) =, B4是坏球偏轻---Answer</font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><font size="3"><span style="mso-fareast-font-family: 'Arial Unicode MS'"><font face="Times New Roman"><span style="mso-spacerun: yes"> </span><span style="mso-spacerun: yes"> </span>if 3) >, B3</font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">是坏球偏轻---Answer</span><span style="mso-fareast-font-family: 'Arial Unicode MS'"></span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><font size="3"><span style="mso-fareast-font-family: 'Arial Unicode MS'"><font face="Times New Roman"><span style="mso-spacerun: yes"> </span>if 3) <, B2</font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">是坏球偏轻---Answer</span></font></p><p style="MARGIN: 5pt 0in; mso-layout-grid-align: none"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span></font></span><span style="display:none;">www.ddhw.com</span><div><strong>第二题：</strong></div><div><div>14只球,外形大小完全相同，前13只球的重量有可能一样,也有可能其中有一只（坏球）偏重，也可能偏轻。第14只球重量跟前面的12只好球一样。也就是说，你事先能确定某一只球是好球。</div><div>现在你用一台天平，找出那只坏球并告诉我它偏轻还是偏重，或者告诉我说跟其余的13只球重量一样。</div><div>请问，至少称多少次可以保证告诉我上面的结果？ <font color="#0000ff">A:3次</font><span style="display:none;">www.ddhw.com</span></div><div><p style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><span style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-fareast-font-family: 'Arial Unicode MS'">Let </span><font size="3"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">第</span><span style="mso-fareast-font-family: 'Arial Unicode MS'"><font face="Times New Roman">14</font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">只好球 = GB</span><span style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-fareast-font-family: 'Arial Unicode MS'"></span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><font size="3"><font face="Times New Roman">Let </font><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">前</span><span style="mso-fareast-font-family: 'Arial Unicode MS'"><font face="Times New Roman">13</font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">只球 = A1A2A3A4A5B1B2B3B4B5C1C2C3; and A12345=A1A2A3A4A5, same as B12345,and<span style="mso-spacerun: yes"> </span>C123</span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3">Weigh 1) A12345 ~ B12345, if 1)=, weigh 2) C12 ~ C3BG, if 2) =, then 坏球跟其余的球重量一样----Answer</font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span>If 2) >, weigh 3) C1 ~ C2, if 3) =, C3是坏球偏轻---Answer</font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span>If 3) >, C1是坏球偏重---Answer</font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span>If 3) <, C2是坏球偏重---Answer</font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span> </font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span>If 1) >, weigh 2) A123B12 ~ C123A45, if 2) =, weigh 3) B3 ~ B4, if 3) =, B5是坏球偏轻---Answer</font></span><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><font size="3"><font face="Times New Roman"><span style="mso-spacerun: yes"> </span><span style="mso-spacerun: yes"> </span>if 3) >, B4</font><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'">是坏球偏轻---Answer</span></font><span style="display:none;">www.ddhw.com</span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span>if 3) <,B3是坏球偏轻---Answer</font></span><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"> </font></span></p><p style="MARGIN: 0in 0in 0pt"><span style="FONT-FAMILY: 'Arial Unicode MS'; mso-hansi-font-family: 'Times New Roman'"><font size="3"><span style="mso-spacerun: yes"> </span></font></span></p></div></div></p></div></div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>

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