A boy and a girl are talking together. The child with black hair says I am a boy. The child with white hair says I am a girl. At least one of these children is lying. In this logic puzzle which child is the boy and which child is the girl?

Introduction / Context:
This is a classic truth and lies puzzle that tests your ability to handle logical statements under the condition that at least one person is lying. The aim is to determine the gender of each child from their statements and from the given condition. Such puzzles are widely used in logical reasoning practice to train systematic case analysis rather than guesswork.

Given Data / Assumptions:
- There are exactly two children, one boy and one girl.- One child has black hair and the other has white hair.- The black haired child says I am a boy.- The white haired child says I am a girl.- It is guaranteed that at least one of the children is lying. It is possible that both are lying.

Concept / Approach:
The approach is to consider all possible assignments of gender to the two children that are compatible with the base information that there is one boy and one girl. For each possible assignment you evaluate whether the two spoken statements become true or false. Then you keep only those assignments that satisfy the extra condition at least one of them lied. By eliminating impossible cases you reach the unique consistent solution.

Step-by-Step Solution:
Step 1: Let B denote the child with black hair and W denote the child with white hair.Step 2: Case one, suppose B is a boy and W is a girl. Then the statement by B I am a boy is true and the statement by W I am a girl is also true. This violates the rule at least one of them lied so this case is impossible.Step 3: Case two, suppose B is a boy and W is a boy. Then the initial condition that there is one boy and one girl is broken so this case is invalid.Step 4: Case three, suppose B is a girl and W is a girl. Again there would be no boy at all so this also contradicts the initial description.Step 5: Case four, suppose B is a girl and W is a boy. Now B says I am a boy, which is false, so B is lying. W says I am a girl, which is also false, so W is lying as well. At least one of them lied is satisfied, and the basic requirement that there is one boy and one girl is also satisfied. So this is the only consistent assignment.

Verification / Alternative check:
You can verify the solution by working backward. If the child with black hair is the girl and the child with white hair is the boy, then both statements in the riddle are lies. The condition at least one is lying allows this possibility. There is no other way to assign genders without either breaking the one boy and one girl requirement or making both statements true. Therefore the conclusion is robust.

Why Other Options Are Wrong:
Option A makes both statements true, which contradicts the given condition that at least one must be lying.Option C and option D both violate the information that there is a boy and a girl, because they suggest two boys or two girls.

Common Pitfalls:
A common mistake is to focus only on the wording at least one lied and overlook the fact that the puzzle also tells us clearly that one child is a boy and the other is a girl. Another mistake is to stop as soon as you find one consistent case without checking all possibilities. Listing all cases and ruling them out systematically is the safest way to handle such logic puzzles.

Final Answer:
The child with black hair is the girl and the child with white hair is the boy.