三年级奥数难题（2023.5.03）：公园游玩 标签：速算与巧算
<p>优学奥数难题以小学4-6年级的杯赛题为来源，试题挑选、答案详解准确性均经优学奥数名师鉴证；根据对历年杯赛真题的研究、总结及归纳，结合了赛题中的高频考点、难点、易错点、以及最近几年命题趋势所得；适合志在杯赛中夺取佳绩的学生。</p><p><strong>有一天，东风东路小学某班50一起去公园游玩。当天他们的上衣不是红色就是黑色，裤子不是蓝色就是黑色。其中有6人穿蓝裤红衣，27人穿黑色裤子，30人穿黑色上衣，那么，有多少人穿黑衣蓝裤呢?</strong></p><p>>>点击查看李佳老师介绍 </p><p>选题编辑：李佳老师</p><p>中山大学本科学历，优学专职教师。文理兼修，喜欢以数学的角度思考生活百态。中学时期曾获希望杯三等奖、国际中小学楚才作文竞赛一等奖、全国英语知识能力竞赛三等奖。</p><p><strong>教学特色：</strong></p><p>讲解细致，条理清晰，认真负责，寓教于乐;理解孩童的思维，擅于用生动活泼的语言引导学生;关心孩子的成长，注重培养学生思考探索的习惯。数学是一件工具，一门语言，更是一种思维方式。数学教会头脑理性、逻辑和缜密，奥数更是集中体现了这些。奥数为孩子打开了一扇门，门外是充满了奇思妙想的世界。我很高兴能带着孩子们欣赏其中的风景。</p><p><strong>老师教你解难题-试题详解</strong></p><p>【分析】根据已知条件可以列出下表</p><p><table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="margin: auto auto auto 50.4pt; width: 262.2pt; border-collapse: collapse;" width="350"><tbody><tr style="height: 13.5pt;"><td nowrap="nowrap" style="border: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; width: 70.85pt; height: 13.5pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-top: 1pt solid windowtext; border-color: windowtext windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="113"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-top: 1pt solid windowtext; border-color: windowtext windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="66"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-top: 1pt solid windowtext; border-color: windowtext windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="76"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td></tr><tr style="height: 23.5pt;"><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-left: 1pt solid windowtext; width: 70.85pt; border-color: rgb(212, 208, 200) windowtext windowtext; border-bottom: 1pt solid windowtext; height: 23.5pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 23.5pt; background-color: transparent;" width="113"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">50</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 23.5pt; background-color: transparent;" width="66"> </td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 23.5pt; background-color: transparent;" width="76"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">30</p></td></tr><tr style="height: 13.5pt;"><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-left: 1pt solid windowtext; width: 70.85pt; border-color: rgb(212, 208, 200) windowtext windowtext; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="113"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">27</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="66"> </td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="76"> </td></tr><tr style="height: 23.7pt;"><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-left: 1pt solid windowtext; width: 70.85pt; border-color: rgb(212, 208, 200) windowtext windowtext; border-bottom: 1pt solid windowtext; height: 23.7pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 23.7pt; background-color: transparent;" width="113"> </td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 23.7pt; background-color: transparent;" width="66"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">6</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 23.7pt; background-color: transparent;" width="76"> </td></tr></tbody></table></p><p>根据表格可以得出以下推理(红色部分)</p><p><table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="margin: auto auto auto 50.4pt; width: 262.2pt; border-collapse: collapse;" width="350"><tbody><tr style="height: 13.5pt;"><td nowrap="nowrap" style="border: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; width: 70.85pt; height: 13.5pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-top: 1pt solid windowtext; border-color: windowtext windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="113"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-top: 1pt solid windowtext; border-color: windowtext windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="66"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-top: 1pt solid windowtext; border-color: windowtext windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="76"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td></tr><tr style="height: 13.5pt;"><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-left: 1pt solid windowtext; width: 70.85pt; border-color: rgb(212, 208, 200) windowtext windowtext; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="113"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">50</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="66"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">50-30=20</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="76"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">30</p></td></tr><tr style="height: 13.5pt;"><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-left: 1pt solid windowtext; width: 70.85pt; border-color: rgb(212, 208, 200) windowtext windowtext; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="113"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">27</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="66"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">20-6=14</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="76"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">27-14=13</p></td></tr><tr style="height: 13.5pt;"><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-left: 1pt solid windowtext; width: 70.85pt; border-color: rgb(212, 208, 200) windowtext windowtext; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="94"><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"></p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 3cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="113"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">50-27=23</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 49.6pt; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="66"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">6</p></td><td nowrap="nowrap" style="border-right: 1pt solid windowtext; padding: 0.75pt 0.75pt 0cm; border-color: rgb(212, 208, 200) windowtext windowtext rgb(212, 208, 200); width: 2cm; border-bottom: 1pt solid windowtext; height: 13.5pt; background-color: transparent;" width="76"><p align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">23-6=17</p></td></tr></tbody></table></p><p>所以，穿蓝裤黑衣的人有17人.</p><p>【总结】容斥原理的题目一般采用画图或者列表的方式解决。</p>
页:
[1]