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abc |
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ab |
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ac |
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ba |
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bc |
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ca |
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cb |
則100a+10b+c=10a+b+10a+c+10b+a+10b+c+10c+a+10c+b,
100a+10b+c=22(a+b+c)
78a=12b+21c
26a=4b+7c
當(dāng)a=1時(shí),b=3,c=2
當(dāng)a=2時(shí),b=6,c=4
當(dāng)a=3時(shí),b=9,c=6
當(dāng)a≥4時(shí),b>10,不合題意.
所以滿足條件的三位數(shù)只有132,264,396.
答:滿足條件的三位數(shù)只有132,264,396.