This is a popular book addressed to a more youthful audience. It really consists of a couple of parts. The first three chapters are a very pleasant discussion of some basic number theory. These form a nice progression. The first is about the interesting property of the decimal number system that the remainder of any positive integer divided by 9 is equal to the remainder of the sum of the digits of the number divided by nine. (This fact is actually slightly misstated in the book, leaving out one of the remainders). The second is about representing numbers in various bases. This chapter demonstrates that the property of 9 discussed in the first chapter can be generalized to different number systems. The third chapter constrasts its subject matter with that of the first, its topic is essential properties of numbers, not those that have to do with the representation. This chapter covers triangular, square, and cubic numbers and interesting relations between them. The basic remarks in this chapter are:
1. There is a CFF formula for the n'th triangular numbers, T(n) = 1 + 2 + ... + n = n (n + 1) / 2.
2. n^2 = 1 + 3 + .. + (2n - 1) or squares can be formed from the sums of sequences of odd numbers.
3. T(n) + T(n + 1) = (n + 1)^2
4. 8 * T(n) + 1 = (2n + 1) ^ 2
5. Every positive integer is the sum of three or fewer triangular numbers and of four or fewer square numbers.
6. Every cube is the difference of two squares; n ^ 3 = T(n) ^ 2 - T(n - 1) ^ 2 I think
7. Consequently 1^3 + 2^3 + .. + n^3 = T(n) ^ 2
Of course, they explain these things in interesting ways rather than just giving you the formula.

The next two chapters are mathematical puzzles, those with numbers and those without.
Chapters 6 and 7 are magic and card tricks based on numbers.
Chapters 8 and 9 are the mathematics of games. ( )