Draw a pressure-volume graph

This is a classic example of a question that may be asked in an oxbridge interview. Getting to the correct answer is certainly not the concern, but the student should think logically of the processes involved in a single heart beat. As long as the student draws a loop of some kind with clear logic at each point of the loop they should be fine. Drawing a single straight line without thought is exactly the kind of behaviour to avoid. The student should always remember to think before answering the question, as this is what happens in supervisions anyways, and the interviewers will expect this of students both in the interview and after.

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Suppose we complete a rectangle of dimensions m*n by the following rule: everytime we complete a square, we put in an number from 0 to 4 equal to the number of adjacent squares already completed. What can we say about the sum of the numbers in all squares


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