Designing a system that will protect an egg dropped from a predefined height is a common experience for many K-12 students and undergraduates in engineering. Often presented in the context of the scientific method, results from these experiments are used to teach concepts of impulse, acceleration, and impact modeling. When done in the classroom, students are usually given a box of pre-defined supplies and a small time frame with which to complete the design. But what educational challenges and outcomes can be gathered from this experience when the problem is tackled using the systematic design process? In this paper, outcomes from the various steps of the design process conducted over a six-week research project by two high school students are presented. Results include the generation of a requirements list, the creation of a functional model, results of brainstorming sessions, concept analysis, model validation through experimentation, optimization, and final design testing. Challenges faced during each step of the design process, and the surprising complexity of the problem, are also discussed. Additionally, the challenges associated with teaching design principles to high school students for a multidisciplinary and multiobjective problem are addressed.