The " third " rightmost digit position contains the values 0 2 0 5 5 2 4 2 7 7 4 6 4 9 9 6 8 6 1 1 8 0 8 3 3 . . . The period is of length 25, and so the probability that the third rightmost digit position is containing the digits 1, 2, 4 or 8 is 11 / 25 = 0.44.
22.
The " third " rightmost digit position contains the values 0 2 0 5 5 2 4 2 7 7 4 6 4 9 9 6 8 6 1 1 8 0 8 3 3 . . . The period is of length 25, and so the probability that the third rightmost digit position is containing the digits 1, 2, 4 or 8 is 11 / 25 = 0.44.
23.
Computing the succesive powers of 16 modulo 100 gives the periodic sequence 16, 56, 96, 36, 76, 16, 56, 96, 36, 76, . . . The period is of length 5, and the probability that the " second " rightmost digit position is containing the digits 1, 2, 4 or 8 is only 1 / 5 = 0.2, ( while a uniform distribution predicts the probability 4 / 10 = 0.4 ).
24.
Moreover, if the sum without a carry is 9 ( in pencil-and-paper methods ) or 1 ( in binary arithmetic ), it is not even possible to tell whether or not a given digit position is going to pass on a carry to the position on its left . At worst, when a whole sequence of sums comes to . . . 99999999 . . . ( in decimal ) or . . . 11111111 . . . ( in binary ), nothing can be deduced at all until the value of the carry coming in from the right is known, and that carry is then propagated to the left, one step at a time, as each digit position evaluated " 9 + 1 = 0, carry 1 " or " 1 + 1 = 0, carry 1 ".
25.
Moreover, if the sum without a carry is 9 ( in pencil-and-paper methods ) or 1 ( in binary arithmetic ), it is not even possible to tell whether or not a given digit position is going to pass on a carry to the position on its left . At worst, when a whole sequence of sums comes to . . . 99999999 . . . ( in decimal ) or . . . 11111111 . . . ( in binary ), nothing can be deduced at all until the value of the carry coming in from the right is known, and that carry is then propagated to the left, one step at a time, as each digit position evaluated " 9 + 1 = 0, carry 1 " or " 1 + 1 = 0, carry 1 ".
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