Answers to problems:
Page 16: '12 × 12 = 144' is a true statement in octal notation because 12 in octal means one eight plus two, which is ten. 144 in octal means one sixty-four plus four eights plus four, which is a hundred.
This is true for numbers to any base of 5 or more, because if n is the base,
(n + 2) × (n + 2) = n² + 4n + 4.
Nine sevens are expressed in binary notation as 1001 × 111. A long multiplication amounts to the addition of 111000 and 111. There is no carrying to be done and the result is 111111.
As a check, 111111 means 32 + 16 + 8 + 4 + 3 + 2 + 1 = 63.
The numbers with pattern 111111...111 in binary notation will make another appearance in chapter 8.
Page 17: The solution to the Killer problem is the same as to the Classic sudoku. Once you have spotted this it makes both problems very easy.