Question 1052975
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Which number {{{highlight(cross(who))}}} when divided by 7,9,11 {{{highlight(cross(and))}}} gives the remainders 1,2,3 {{{highlight(respectively)}}}?
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The numbers that give the remainder 1 when divided by 7, form an arithmetic progression 

1, 8, 15, 22, 29, . . . (1 + 7(n-1)), . . . 

Of these numbers, the smallest number that gives the remainder 2 when divided by 9, is {{{highlight(29)}}}.


Next, the numbers that give the remainder 1 when divided by 7 and the remainder 2 when divided by 9, form an arithmetic progression 

29, 29+63 = 92, 29+2*63 = 155, 29+3*63 = 218,  . . . (29+(n-1)*63), . . . 
  (notice: 63 = 7*9)

Among them, the smallest number that gives the remainder 3 when divided by 11, is {{{highlight(344)}}}.

<U>Answer</U>.  Your number is 344.
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