Modeling Difficult

Lecture Notes

This is an advanced technique. Its core idea is to translate a difficult problem into an easier problem. If these two problems have a one-to-one mapping, then their counts must be equal. To be proficient in using this method, you needs to be first familiar with various well-known patterns, techniques, and problems, and then have the ability to connect the dots by recognizing the same nature of different problems. (Remember what we have talked about in the lesson Count Like A Pro?)


Examples

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Let $N$ be the number of possible ways to pick up two adjacent squares in a $(n\times m)$ grid. Find $N$.