Question 1135926
let the digits be xyz, then
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1) 100x +10y +z = 11 * (x +y +z)
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(100x +10y +z)/11 = x +y +z
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The divisibility rule for 11 is that the alternating sum of the digits must be a multiple of 11, that is
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x -y +z = 11k, for some integer k
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Note that 11k can be 0 or 11 only, just consider values of x, y, z
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If k = 0, then
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y = x+z
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substitute for y in equation 1 and we get
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z = 8x implies that y = 9x
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so we have 198, with x = 1 and 198 satisfies 1 -9 +8 = 0
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for k = 0, we have 198
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if k = 1, then
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x -y +z = 11
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y = x +z -11
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substitute for y in equation 1 and we get
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z = 8x +1, implies y = 9x -10
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if x is 1 then y is -1 and if x = 2, then z = 11
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there is no solution for k = 1
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