What does that sign mean?

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We define # , as following 3 3 # = 6 =6 ; 45 45 # = 99 =99 ; 432 432 # = 666 =666 ; 431 431 # = 565 =565 Find the sum of digits of 987654321 987654321 #


The answer is 9.

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2 solutions

If we let a a and b b be digits of a number, a b ab # = a b + b a =ab+ba . So 987654321 987654321 # = 987654321 + 123456789 = 1111111110 =987654321+123456789=1111111110

Maggie Miller
Aug 3, 2015

Given digits a 1 , , a n a_1,\ldots,a_n , a 1 a n # = b 1 b n \overline{a_1\cdots a_n}\#=\overline{b_1\cdots b_n} , where b k = a k + a n + 1 k b_k=a_k+a_{n+1-k} .

Therefore, 987654321 # = 101010101010101010 987654321\#=101010101010101010 , so the answer is 9 \boxed{9} .

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