InterviewSolution
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InterviewSolution
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Show that one and only one out of `n`, `n +1` and `n +2` is divisible by `3`, where `n` is any positive integer. |
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Answer» On dividing n by 3, let q be the quotient and r be the remainder . Then, n = 3q +r , where `0 ge r gt 3` ` Rightarrow n = 3q + r , " where r " = 0 ,1 or 2 ` m ` Rightarrow n = 3q +r or n ( 3q +1) or n = ( 3q +2)` Case I If n = 3q then n is clearly divisible by 3. Case II If n= ( 3q +1) then ( n+2) = (3q +3) = 3(q +1) , which is clearly divisible by 3. In this case, ( n+2) is divisble 3. Case III If n = ( 3n +2) then (n+1) = ( 3q +3) = 3(q +1) , whihc is clearly divisible by 3. In this case, (n+2) is divsible by3 . In this case , (n +1) is divisible by3. Hence, one and only one out of n,( n +1) and (n+2) is divisible by 3. |
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