Get enough hard-boiled eggs for each participant to have one. If you want to add a crafty element you can have the kids decorate or personalize their eggs. Set up a start and finish line outdoors for older kids but it can be played indoor if the racers are very young. The object of the game is for the kids to push their egg across the finish line. The trick is that they cannot use their hands or feet to push the egg, so they can use their elbows, knees, nose or anything else not at the end of their arms or legs. The first person to push the egg across the finish line is the winner and awarded a prize.
TIP: If you want to increase the challenge and have enough room you can add some obstacles to the race route or require them to zigzag around a predetermine course.