Tug of War
Test which gender has greater physical strength with Tug of War. Lay out two parallel lines 20 feet apart on a grass field or draw them in dirt. Lay a rope perpendicular to these lines. Make sure the rope is made of natural fiber, as synthetic fiber can snap back and cause serious damage to children. Tie a cloth flag to the rope's middle. Choose two even teams of boys and girls. For example, one side can have three boys and the other can have three girls. Position them along the rope behind each of the parallel lines, leaving the space between the lines empty. The team that pulls the cloth flag over their line first wins.
Boys and girls can go against each other to see who has the better hiding skills. Choose a safe place for the kids to play in, with many different hiding spaces. Have one gender go and hide in these spaces while the other gender looks away and counts down from a set number. For instance, the boys can count down from 30 while the girls run and hide, then look for them afterward. After all the girls are found, the teams switch roles -- the girls will then count down from 30, while the boys find hiding spots.
Alphabet Soup is similar in nature to Scrabble. Split your group into boys and girls. Give them plates and some Alphabet Soup cans. A less messier alternative can be any cereal brand with edible letters. Teams go through the letters to make words. Make up your own point system and award points based on the number of letters used in each word. For example, you could set 50 as a point limit. Give five points for five letter words, four points for four letter words and three points for three letter words. The group with the higher point accumulation after a given time frame wins.
Water Gun Fight
Organize a water fight between the boys and girls. Choose a safe, open field with as few obstacles as possible. Have the youth bring in their own water guns or provide guns for them. You can award points based on how the teams soak one another with water. For instance, if a girl shoots a boy in the chest, she can receive 10 points, whereas a direct shot to the leg can garner 5 points. Have people watching from the sidelines to oversee the action and keep tabs on where the kids are hitting one another. You can also judge it based on which team is more wet by the fight's end, or alter the rules to your liking.