TH

Nếu abcd +  bcda +  cdab + dabc = 17776. Tính a + b + c + d

H24
1 tháng 12 lúc 10:30

\(abcd=1000a+100b+10c+d\\ bcda=1000b+100c+10d+a\\ cdab=1000c+100d+10a+b\\ dabc=1000d+100a+10b+c\\ abcd+bcda+cdab+dabc=1000a+100b+10c+d+1000b+100c+10d+a+1000c+100d+10a+b+1000d+100a+10b+c\\ 1111a+1111b+1111c+1111d=1111\left(a+b+c+d\right)\)

mà tổng này là 17776 nên 

\(1111\left(a+b+C+d\right)=17776\\ a+b+c+d=\dfrac{177766}{1111}=16\)

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