number of 6s = 5 0 6 − 6 − 6 − ⋯ − 6 = number of 9s = N 9 − 9 − 9 − ⋯ − 9
What is N ?
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We can evaluate the first 2 terms on either side to equal 0. This means that we are left with 4 8 × − 6 on the left hand side and ( N − 2 ) × − 9 on the right. Therefore, 4 8 × − 6 = − 9 ( N − 2 ) − 2 8 8 = − 9 ( N − 2 ) 3 2 = N − 2 N = 3 4
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number of 6’s = 5 0 6 − 6 − 6 − ⋯ − 6 = number of 9’s = N 9 − 9 − 9 − ⋯ − 9 6 − 6 ( number of 1’s = 4 9 1 + 1 + 1 ⋯ + 1 ) = 9 − 9 ( number of 1’s = x ( s a y ) 1 + 1 + 1 + ⋯ + 1 ) From above we get . 6 − 6 . 4 9 = 9 − 9 x − 6 . 4 8 = 9 ( 1 − x ) ⇒ x = 3 3 So required numbers of N = 3 4 since N = x + 1 .