YLL討論網

嗯！沒錯。關鍵的確是在２５和２２５。 您完整的答對了。

#ed_op#DIV#ed_cl#有數字為9的平方數字依序為9,49,169,196,289,...#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#因為9的前後數都需有數字9為伴，故k最小至少為13#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#而小於等於13的平方數中，有數字為2的平方數字僅有25,121，有數字為5的平方數字僅有25#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#故最小存在可能時121必與25相鄰，則25之另一鄰居則尚缺，故需尋找其後有2或有5的平方數字，故此時k最小已為15#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#故最小存在可能時，121,25,225必為相鄰，但225之另一鄰居已無2或5與之相配，故需再往後借位，故此時k最小已為16#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#依題意將此16數排進圓內#ed_op#/DIV#ed_cl#

能不能證明或說明１６是最小解呢？

#ed_op#DIV#ed_cl#k=16#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#以下為其一排法#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#TABLE style="WIDTH: 54pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=72 border=0 x:str#ed_cl##ed_op#COLGROUP#ed_cl##ed_op#COL style="WIDTH: 54pt" width=72#ed_cl##ed_op#TBODY#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 54pt; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right width=72 height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#81#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#144#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#4#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#49#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#9#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#169#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#121#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#25#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; 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BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#36#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#16#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#1#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#100#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#TR style="HEIGHT: 16.5pt" height=22#ed_cl##ed_op#TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" align=right height=22 x:num#ed_cl##ed_op#FONT face=新細明體#ed_cl#81#ed_op#/FONT#ed_cl##ed_op#/TD#ed_cl##ed_op#/TR#ed_cl##ed_op#/TBODY#ed_cl##ed_op#/TABLE#ed_cl##ed_op#/DIV#ed_cl#

不是20

Ｋ最小為２０

某人把平方數１、４、９、１６、…、ｋ^２（其中ｋ＞１）放在一個圓的圓周上，使得圓周上任何兩個相鄰的平方數都最少有一個數字相同（例如１和１６皆有數字’１’）．求ｋ的最小可能值。