Patrick's Joyful Encounter with the Elf
Patrick was ecstatic to see the elf for several reasons that encapsulated the essence of his character and his situation.

Relief from Homework
- Patrick was overwhelmed with the burden of homework.
- He had a strong dislike for studying and found it tedious.
- The appearance of the elf presented an unexpected solution to his problems.

Magical Assistance
- The elf promised to help Patrick with his homework.
- This magical assistance was a dream come true for someone who dreaded academic tasks.
- The prospect of getting his homework done effortlessly filled Patrick with happiness.

Friendship and Companionship
- The elf’s presence brought a sense of companionship to Patrick.
- He felt less alone in his struggles, knowing he had someone to rely on.
- This bond transformed his negative feelings about homework into a more positive experience.

Unexpected Turn of Events
- Initially, Patrick's happiness was rooted in the elf's help.
- However, as the story progresses, he realizes that the elf's methods were unconventional and chaotic.
- This twist added humor to the narrative and ultimately taught Patrick the importance of hard work and diligence.

Conclusion
In summary, Patrick's joy at seeing the elf stemmed from his desire to escape the burdens of homework, the allure of magical help, and the companionship that came with the encounter. Despite the challenges that followed, this experience shaped his outlook on education and effort.