In a used book store, there are some different mystery novels on a shelf. Suppose there are 64 different ways to buy these novels, including not buying any of them. How many mystery novels are there on the shelf?

To find out how many mystery novels there are on the shelf given that there are 64 different ways to buy them, we can use the concept of combinations where the order of selection does not matter, and we account for the possibility of buying zero, one, or more novels.

Since each novel can either be bought or not bought, for n novels, there are 2^n different combinations of buying the novels (since every novel has two states - either included in the purchase or not). This includes the possibility of not buying any novels (which is one of the combinations).

Given 2^n = 64, we need to solve for n to determine the number of novels.

We can express 64 as a power of 2 since 64 is a power of 2 itself: 64 = 2^6

Therefore, we can set up the equation: 2^n = 2^6

Since the bases are equal (both are 2), their exponents must be equal as well for the equation to hold true.

So, n = 6

This means there are 6 mystery novels on the shelf.