看看下列有趣的式子： 12×42=21×24是否有其他二位數也可以有
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[轉貼]有趣的式子
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由 小鳴 於 星期二 三月 09, 2004 11:06 pm
設兩數為(10a+b),(10c+d),
1≦a≦9,1≦b≦9,1≦c≦9,1≦d≦9
(10a+b)(10c+d)=(10b+a)(10d+c)
100ac+10bc+10ad+bd=100bd+10ad+10bc+ac
99ac=99bd
ac=bd
由此可見,只要兩個十位數相乘等於兩個個位數相乘便是答案.答案如下:
11×11=11×11,12×21=21×12,13×31=31×13,14×41=41×14,
15×51=51×15,16×61=61×16,17×71=71×17,18×81=81×18,
19×91=91×19,
22×22=22×22,23×32=32×23,24×42=42×24,
25×52=52×25,26×62=62×26,27×72=72×27,28×82=82×28,
29×92=92×29,
33×33=33×33,34×43=43×34,
35×53=53×35,36×63=63×36,37×73=73×37,38×83=83×38,
39×93=93×39,
44×44=44×44,
45×54=54×45,46×64=64×46,47×74=74×47,48×84=84×48,
49×94=94×49,
55×55=55×55,56×65=65×56,57×75=75×57,58×85=85×58,
59×95=95×59,
66×66=66×66,67×76=76×67,68×86=86×68,
69×96=96×69,
77×77=77×77,78×87=87×78,
79×97=97×79,
88×88=88×88,
89×98=98×89,
99×99=99×99,
(廢話
)
21×24=12×42,21×36=12×63,26×31=62×13,21×48=12×84,
28×41=82×14,24×63=42×36,23×64=32×46,24×84=42×48,
23×96=32×69,26×93=62×39,31×39=13×93,36×84=63×48,
34×86=43×68,46×96=64×69
1≦a≦9,1≦b≦9,1≦c≦9,1≦d≦9
(10a+b)(10c+d)=(10b+a)(10d+c)
100ac+10bc+10ad+bd=100bd+10ad+10bc+ac
99ac=99bd
ac=bd
由此可見,只要兩個十位數相乘等於兩個個位數相乘便是答案.答案如下:
11×11=11×11,12×21=21×12,13×31=31×13,14×41=41×14,
15×51=51×15,16×61=61×16,17×71=71×17,18×81=81×18,
19×91=91×19,
22×22=22×22,23×32=32×23,24×42=42×24,
25×52=52×25,26×62=62×26,27×72=72×27,28×82=82×28,
29×92=92×29,
33×33=33×33,34×43=43×34,
35×53=53×35,36×63=63×36,37×73=73×37,38×83=83×38,
39×93=93×39,
44×44=44×44,
45×54=54×45,46×64=64×46,47×74=74×47,48×84=84×48,
49×94=94×49,
55×55=55×55,56×65=65×56,57×75=75×57,58×85=85×58,
59×95=95×59,
66×66=66×66,67×76=76×67,68×86=86×68,
69×96=96×69,
77×77=77×77,78×87=87×78,
79×97=97×79,
88×88=88×88,
89×98=98×89,
99×99=99×99,
(廢話
)
21×24=12×42,21×36=12×63,26×31=62×13,21×48=12×84,
28×41=82×14,24×63=42×36,23×64=32×46,24×84=42×48,
23×96=32×69,26×93=62×39,31×39=13×93,36×84=63×48,
34×86=43×68,46×96=64×69
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小鳴 - 訪客
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