四四 2007-5-12 02:14
傅乐数学题答案
<p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">数学题答案</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">:(20</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">分</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">)<p></p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><span style="mso-spacerun: yes;"> </span><p></p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><br/>1.</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">用一架普通的天平分別稱出</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">1</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">克，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">2</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">克，……，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">123</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">克，共</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">123</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">個不同物體的重量；</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">那麼，最少需要幾個天平砝碼？（</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">3</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">分）砝碼各重多少克？（</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">3</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">分）</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">用上述最少的那幾個砝碼，一直可以稱量到幾克的物體（物體的重量為連續自然數）（</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">4</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">分）？</span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"></span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">5</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">個，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">2</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">6</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">18</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">54</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">162</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">……</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">243</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">克</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><p> </p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">2.</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">在</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">(0</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">，</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">L)</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">之間任意取兩點，則兩點之間的距離小于</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">L/3</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">的概率為</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">________</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">．（</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">5</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">分）請給出必要的計算步驟（</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">5</span><span lang="ZH-TW" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;">分）</span><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN; mso-fareast-language: ZH-TW;"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN;"></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN;">5/9 </span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN;"></span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 宋体; mso-ansi-language: ZH-CN;"><strong><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-bidi-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-ascii-font-family: ˎ̥; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">注:以上是评委收到的原文，赛场公布的题目是经过评委修改后的版本。</span></strong></span></p>
四四 2007-5-12 02:15
<p style="BACKGROUND: white; WORD-BREAK: break-all;"><span lang="ZH-CN" style="COLOR: #f73809; FONT-FAMILY: 宋体;">小泥巴队</span><span style="COLOR: #f73809; FONT-FAMILY: 宋体;"><p></p></span></p><p style="BACKGROUND: white; WORD-BREAK: break-all;"><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">9</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">个砝码。分别为：</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">1</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">2*2</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">5</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">10</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">2*20</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">2*50</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span lang="ZH-CN" style="COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman";">把砝</span><span lang="ZH-CN" style="COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">码</span><span lang="ZH-CN" style="COLOR: red; FONT-FAMILY: "MS Mincho"; mso-bidi-font-family: "MS Mincho";">全部加起来</span><span lang="ZH-CN" style="COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">为</span><span lang="ZH-CN" style="COLOR: red; FONT-FAMILY: "MS Mincho"; mso-bidi-font-family: "MS Mincho";">最重称重量。</span><span style="COLOR: red; FONT-FAMILY: Tahoma; mso-bidi-font-size: 9.0pt;"><p></p></span></p><p style="BACKGROUND: white; WORD-BREAK: break-all;"><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">最大称重</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">为</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">：</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">160</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克。</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><p></p></span></p><p style="BACKGROUND: white; WORD-BREAK: break-all;"><b><span style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">0</font></span></b><b><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: "Times New Roman"; mso-ascii-font-family: "Times New Roman";">分</span><span style="COLOR: lime;"><p></p></span></b></p>
四四 2007-5-12 02:18
<p>饭桶队<br/>数学<br/>1 至少需要6个砝码。分别为1，3，9，27，81，243克<br/> 用这些砝码，可以称1+3+9+27+81+243=364克的物品。</p><p>2 <br/>答案：7/16 <br/>取L为1，即求两数x,y,∈（0，1）。为使 |x-y|<1/4, 分段考虑 <br/>当x∈(0 , 1/4)的1/4区间，y的取值范围在(0, x+1/4); <br/>当x∈（1/4，1/2）长度为1/4的区间，y 的取值范围在(x-1/4, x+1/4),长度为1/2的区间。 <br/>根据对称性，1/2< x < 1情况的概率同上 <br/>计算概率 [attach]7066[/attach]<br/>计算结果得7/16 </p><strong><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-ascii-font-family: ˎ̥; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">第</span><span style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-fareast-font-family: 宋体; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"><font face="Times New Roman">2</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-ascii-font-family: ˎ̥; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">题</span><span style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-fareast-font-family: 宋体; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"><font face="Times New Roman">10</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-ascii-font-family: ˎ̥; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">分</span></strong><br/>
四四 2007-5-12 02:18
<p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">通吃队</span></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span lang="ZH-CN" style="FONT-SIZE: 10pt; COLOR: red; FONT-FAMILY: 宋体; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;"></span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">1.</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">共需要</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">6</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">个砝</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">码</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">，分</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">别</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">是</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">1</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">3</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">9</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">27</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克，</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">81</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克和</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">243</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">.</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">可以称出</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">1</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">至</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">364</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">克的物体</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><br/><font face="Times New Roman">2.7/16</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">，可以建立一个平面直角坐</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">标</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">系，任意两点分</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">别</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">在</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">x,y</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">轴</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">上，并且</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">0<x<1,0<y<1,</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">满</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">足</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">│x-y│<1/4</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">，所以</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">x,y</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">组</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">成的</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">线</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">段落在直</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">线</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">x-y=1/4</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">和</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">x-y=-1/4</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">之</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">间</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">的区域</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">,</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">求出</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">这</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">部分区域的面</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">积</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;"><font face="Times New Roman">,</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Mincho"; mso-hansi-font-family: ˎ̥; mso-ascii-font-family: ˎ̥;">再除以正方形面</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">积</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: "MS Gothic"; mso-bidi-font-family: "MS Gothic";">就得到概率</span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: MingLiU; mso-bidi-font-family: MingLiU;">为</span><font face="Times New Roman"><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥;">7/16.</span><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥; mso-fareast-font-family: 宋体;"><p></p></span></font></p><p class="MsoNormal" style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none;"><span style="FONT-SIZE: 10.5pt; COLOR: red; FONT-FAMILY: ˎ̥; mso-fareast-font-family: 宋体;"><p><font face="Times New Roman"> </font></p></span></p><b><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-ascii-font-family: ˎ̥; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">第</span><span style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-fareast-font-family: 宋体; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"><font face="Times New Roman">2</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-ascii-font-family: ˎ̥; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">题</span><span style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-fareast-font-family: 宋体; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"><font face="Times New Roman">10</font></span><span lang="ZH-CN" style="FONT-SIZE: 10.5pt; COLOR: lime; FONT-FAMILY: 宋体; mso-hansi-font-family: ˎ̥; mso-bidi-font-family: "Times New Roman"; mso-ansi-language: EN-US; mso-ascii-font-family: ˎ̥; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">分</span></b>
