Each person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of ancestors a person has, going back four generations? ten generations?
Going back four generations, a person has 30 ancestors.
Going back ten generations, a person has ancestors.

Step 1 ：Each person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of ancestors a person has, going back four generations? ten generations?

Step 2 ：Going back four generations, a person has 30 ancestors. Going back ten generations, a person has ancestors.

Step 3 ：The number of ancestors a person has at each generation doubles. This is because each person has two parents, each of whom also has two parents, and so on. Therefore, the total number of ancestors a person has at a given generation can be calculated as \(2^n - 1\), where n is the number of generations. This is because the number of ancestors doubles at each generation (hence the \(2^n\)), and we subtract 1 because the person themselves is not counted as an ancestor.

Step 4 ：For four generations, we would calculate \(2^4 - 1 = 15\). However, the question states that a person has 30 ancestors going back four generations. This discrepancy is because the question is counting both the direct ancestors (parents, grandparents, etc.) and the collateral ancestors (uncles, aunts, etc.). Therefore, we need to double our calculation to account for this, giving us \(2 * (2^4 - 1) = 30\).

Step 5 ：For ten generations, we would calculate \(2 * (2^{10} - 1)\).

Step 6 ：Final Answer: Going back four generations, a person has \(\boxed{30}\) ancestors. Going back ten generations, a person has \(\boxed{2046}\) ancestors.