數列謎題解析--GameSchool遊戲學校

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數列 - 謎題解析

定義Sn為此數列的前n項和。
根據條件1可列出：
S5&gt;0，S6-S1&gt;0，S7-S2&gt;0，S8-S3&gt;0，S9-S4&gt;0，S10-S5&gt;0，S11-S6&gt;0，S12-S7&gt;0
根據條件2可列出：
S9&lt;0，S10-S1&lt;0，S11-S2&lt;0，S12-S3&lt;0
把這些條件合起來就是：
S8&gt;S3&gt;S12&gt;S7&gt;S2&gt;S11&gt;S6&gt;S1&gt;S10&gt;S5&gt;0&gt;S9&gt;S4
由於這是一個整數數列，Sn必定也是整數，因此S8&gt;=10，S4&lt;=-2，
再配上條件3：S8-S4=12，S1到S12現在只有一種可能：
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="font-family:'Times New Roman';border:none;width:500px;"><tr><td style="width:34.8pt;border:1pt solid;padding:0cm 5.4pt;">n
</td>
<td style="width:34.8pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">1
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">2
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">3
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">4
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">5
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">6
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">7
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">8
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">9
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">10
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">11
</td>
<td style="width:34.85pt;border-style:solid solid solid none;border-top-width:1pt;border-right-width:1pt;border-bottom-width:1pt;padding:0cm 5.4pt;">12
</td>
</tr><tr><td style="width:34.8pt;border-style:none solid solid;border-right-width:1pt;border-bottom-width:1pt;border-left-width:1pt;padding:0cm 5.4pt;">Sn
</td>
<td style="width:34.8pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">3
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">6
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">9
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">-2
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">1
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">4
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">7
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">10
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">-1
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">2
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">5
</td>
<td style="width:34.85pt;border-style:none solid solid none;border-bottom-width:1pt;border-right-width:1pt;padding:0cm 5.4pt;">8
</td>
</tr></table>因此這個數列是：
3,3,3,-11,3,3,3,3,-11,3,3,3

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