  # For first 10 positive integers find a number as product of numbers before that is same as product of numbers after it?

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1, 2, 3, 4, 5, 6, 7, 8, 9, 10
The above are the first 10 positive integers. The product of the numbers before the number __ is the same as the product of the numbers after that number. posted Sep 13, 2017

Before 7 product is 6*5*4*3*2*1 = 720
and after 7 product is 8*9*10 = 720
The product of the numbers before the number ** 7 ** is the same as the product of the numbers after that number. answer Sep 13, 2017

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An automorphic number is a number whose square ends in the same digits as the number itself. For example, the number 25 is an automorphic number (in base 10) because its square, 625, ends with the original number.

For the first 100 positive integers, five numbers are automorphic numbers for base 10 (1, 5, 6, 25, and 76), while only one number is automorphic for base 2 (1).

Which of the following bases has the most automorphic numbers for the first 100 positive integers?

a) 15
b) 6
c) 12
d) 7
e) 10