In English idioms, what does the expression "to have something on the brain" mean, when someone keeps thinking about the same thing again and again?

Introduction / Context:
This question tests understanding of a common English idiom from everyday speech. When native speakers say that someone has something on the brain, they are using a vivid image to describe how a single idea or topic keeps dominating that person's thoughts. Recognising this meaning is important for reading conversations, novels, and newspapers where such informal expressions appear frequently.

Given Data / Assumptions:
- Target idiom: "to have something on the brain". - Context: used about a person who keeps thinking about the same topic. - Four possible meanings are offered, all related to thinking or mental activity. - We must choose the meaning that best matches real idiomatic usage.

Concept / Approach:
Idioms often cannot be understood by translating each individual word literally. Here the word brain suggests the mind or thinking, and have something on the brain suggests that a particular thought is sitting there all the time. In natural English this idiom is used when someone is almost obsessed with a hobby, problem, person, or plan. They talk about it constantly and find it hard to think about anything else.

Step-by-Step Solution:
Step 1: Focus on the key image. "On the brain" suggests that a thought is stuck in a person's mind. Step 2: Recall typical usage: "He has football on the brain" or "She has exams on the brain". In such sentences it clearly means they are thinking about that thing all the time. Step 3: Compare this with option A, "To be obsessed with something". Obsession is a strong, repeated focus on one thing. Step 4: Compare with the other options and see that they describe different ideas, such as being witty or thinking about the past. Step 5: Conclude that option A captures the idiom accurately.

Verification / Alternative check:
You can test the options by inserting them back into a sample sentence. For example, "He has cricket on the brain these days" is naturally paraphrased as "He is obsessed with cricket these days." None of the other meanings fit smoothly. It would sound strange to say that the idiom means he is "ready with a witty reply" or "unable to solve a philosophical problem". This confirms that obsession or constant concern is the correct interpretation.

Why Other Options Are Wrong:
Option B, about being ready with a witty reply, describes quick humour, not continuous thinking about one topic. Option C, about failing to solve a philosophical problem, focuses on difficulty rather than repeated attention. Option D, about thinking wistfully about past life, suggests nostalgia, which is different from being fixated on any kind of subject.

Common Pitfalls:
Learners sometimes overthink idioms and connect them to deep philosophy because of the word brain. Remember that many idioms are informal and colourful rather than scientific. Linking this expression with everyday examples such as hobbies, sports, or relationships will help you recall that it means being obsessed or preoccupied, not simply being intelligent or thoughtful.

Final Answer:
"To have something on the brain" means to be obsessed with something, that is, to keep thinking about it all the time.