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标题: 【求助】一道数学题，求解。 [打印本页]

作者: xfbfj 时间: 2006-1-16 21:23
标题: 【求助】一道数学题，求解。
一道数学题，求解。5人分桃，怎么也分不公平。一人偷偷地拿了一个桃扔了，把剩下的5等份，拿走了一份。第二个人也偷偷地扔了一个，剩下的5等份，也拿走了一份。以此类推，另外三个人也是这样依次扔掉一个桃子，还能分成5等份。请问，原来这堆桃子至少有多少个？

作者: 无可奈何 时间: 2006-1-17 00:46
闲来无事,瞎解一通,不知正确否,sum=5a+14a=5b+14b=5c+14c=5d+14d=5e+1因此,sum=e*3125/256+2101/256,该sum为正整数,等式最小的解为e=255,故sum=3121,附带,此题发到小学数学恐怕不妥当,哈。

作者: xfbfj 时间: 2006-1-17 14:45
这是小学六年级寒假作业里的题目。你做的可能不对。验算通不过啊。不过我也不会。

作者: 无可奈何 时间: 2006-1-17 15:11
验算能通过,呀。

作者: 儿教 时间: 2006-1-17 15:43
5人分桃，怎么也分不公平。一人偷偷地拿了一个桃扔了，把剩下的5等份，拿走了一份。第二个人也偷偷地扔了一个，剩下的5等份，也拿走了一份。以此类推，另外三个人也是这样依次扔掉一个桃子，还能分成5等份。请问，原来这堆桃子至少有多少个？至少多少个??对不对,,,,第五次还能分成5等份,那么最后就是5个咯第四次,丢了一个,还能分了五分,,,,就 (5+1)*5第三次，丢了一个,还能分五分,,,,就((5+1)*5+1)*5类推下去((((5+1)*5+1)*5+1)*5+1)*5+1=3906

作者: 无可奈何 时间: 2006-1-17 16:33
第一,原题目中有拿走一份,剩下4份,再分的话，第二,第五个人分的时候也是先扔了一个的，

作者: sxchd 时间: 2006-1-17 18:40
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">答案3121,验证如下.但对小学生确实有些难!</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt"></span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">分之前的数<span lang="EN-US"><span style="mso-tab-count: 1"> </span></span>仍掉<span lang="EN-US">1</span>后的数<span lang="EN-US"><span style="mso-tab-count: 1"> </span></span>分成五份每份的数<span lang="EN-US"><span style="mso-tab-count: 1"> </span></span>拿走一份后数<span lang="EN-US"></span></span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">1<span style="mso-tab-count: 1"> </span>3121<span style="mso-tab-count: 1"> </span>3120<span style="mso-tab-count: 1"> </span>624<span style="mso-tab-count: 1"> </span>2496</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">2<span style="mso-tab-count: 1"> </span>2496<span style="mso-tab-count: 1"> </span>2495<span style="mso-tab-count: 1"> </span>499<span style="mso-tab-count: 1"> </span>1996</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">3<span style="mso-tab-count: 1"> </span>1996<span style="mso-tab-count: 1"> </span>1995<span style="mso-tab-count: 1"> </span>399<span style="mso-tab-count: 1"> </span>1596</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">4<span style="mso-tab-count: 1"> </span>1596<span style="mso-tab-count: 1"> </span>1595<span style="mso-tab-count: 1"> </span>319<span style="mso-tab-count: 1"> </span>1276</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">5<span style="mso-tab-count: 1"> </span>1276<span style="mso-tab-count: 1"> </span>1275<span style="mso-tab-count: 1"> </span>255<span style="mso-tab-count: 1"> </span></span>

作者: sxchd 时间: 2006-1-17 18:50

sxchd+2006-01-17 18:40-->引用:sxchd @ 2006-01-17 18:40 <p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">答案3121,验证如下.但对小学生确实有些难!</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt"></span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">分之前的数<span lang="EN-US"><span style="mso-tab-count: 1"> </span></span>仍掉<span lang="EN-US">1</span>后的数<span lang="EN-US"><span style="mso-tab-count: 1"> </span></span>分成五份每份的数<span lang="EN-US"><span style="mso-tab-count: 1"> </span></span>拿走一份后数<span lang="EN-US"></span></span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">1<span style="mso-tab-count: 1"> </span>3121<span style="mso-tab-count: 1"> </span>3120<span style="mso-tab-count: 1"> </span>624<span style="mso-tab-count: 1"> </span>2496</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">2<span style="mso-tab-count: 1"> </span>2496<span style="mso-tab-count: 1"> </span>2495<span style="mso-tab-count: 1"> </span>499<span style="mso-tab-count: 1"> </span>1996</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">3<span style="mso-tab-count: 1"> </span>1996<span style="mso-tab-count: 1"> </span>1995<span style="mso-tab-count: 1"> </span>399<span style="mso-tab-count: 1"> </span>1596</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">4<span style="mso-tab-count: 1"> </span>1596<span style="mso-tab-count: 1"> </span>1595<span style="mso-tab-count: 1"> </span>319<span style="mso-tab-count: 1"> </span>1276</span><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 4.4pt; TEXT-ALIGN: left; mso-pagination: widow-orphan; tab-stops: 41.4pt 128.4pt 212.4pt 320.4pt" align="left"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-font-kerning: 0pt">5<span style="mso-tab-count: 1"> </span>1276<span style="mso-tab-count: 1"> </span>1275<span style="mso-tab-count: 1"> </span>255<span style="mso-tab-count: 1"> </span></span>

总数=<span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman"; mso-font-kerning: 1.0pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">((((5×a+1)÷4×5+1)÷4×5+1)÷4×5+1)÷4×5+1=(3125a+2101)</span><span style="FONT-SIZE: 22pt; FONT-FAMILY: 宋体; mso-bidi-font-family: "Times New Roman"; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"">÷</span><span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman"; mso-font-kerning: 1.0pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">256<span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman"; mso-font-kerning: 1.0pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">=(3125a+2101)</span><span style="FONT-SIZE: 22pt; FONT-FAMILY: 宋体; mso-bidi-font-family: "Times New Roman"; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"">÷</span><span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman"; mso-font-kerning: 1.0pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">256</span></span><span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman"; mso-font-kerning: 1.0pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman"; mso-font-kerning: 1.0pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">求最小的a为255,总数为3121.</span></span>

作者: 无可奈何 时间: 2006-1-17 21:25
怎么样让一个小学六年级的学生理解这个,确实是问题,不知论坛有否小学数学老师,哈,

作者: 魔王 时间: 2006-1-19 17:42
中学题。

作者: 661013 时间: 2006-1-21 00:08
用倒推法解倒1剩6个倒2剩6*5+1=31倒3剩31*5+1=156倒4剩156*5+1=781倒5剩781*5+1=3906这应该是一道小学三年级-----用倒推法解应用题的奥数题。

作者: jingling81 时间: 2006-1-21 09:39
看着是奥数题

作者: qdylz 时间: 2011-3-30 16:15
感觉数字有些大，没有数字小一点的解法吗？

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