So, this is one of the things I totally thought was a universal pastime, and then I talked about it in America and people stared at me with blank faces. So I am guessing it is not.
The game is called Számháború (Number War)
If you want to name a game that a large number of people can play out in the open for long periods of time, this is that game. We have all played it at one point or another, waaay before laser tag and paintball ever came along. The upside is that it barely requires any supplies (and definitely no guns, fake or otherwise), which makes it very child-friendly.
(It also exhausts the little critters thoroughly, which parents appreciate)
Step 1: Recruit people, and find a place to play. The more objects (trees, rocks, structures) in the area, the better.
Step 2: Divide people into two groups. Mark them somehow (red shirts vs blue shirts, etc.)
Step 3: Everyone gets a headband with a (4 or 5 digit) number on it. Make sure everyone remembers their OWN number correctly. Also make sure the teams don't put on their numbers until they are well away from each other.
Step 4: If you want, you can play it capture-the-flag style and have both teams hide a flag somewhere. Or you can just play it as "last man standing."
Step 5: Set the teams loose in the area. The goal is to pick off the opposing team's players by reading their number out loud. If you hear your number yelled, you are dead/out.
The fun of the game mostly comes from techniques of moving without revealing the number on your forehead. It is not allowed to cover it, or put your hand/arm over it - but taking cover in other ways is fair game. People have their own techniques of doing this:
Some lean their foreheads against trees while the enemy passes
others put their face on the ground and progress inchworm-style,
sneak in tall grass,
or try to run in a straight line while vigorously shaking their head,
or put their foreheads together and try to run that way.
As you can see from these examples, the game mostly results in hilarity, and a lot of yelling; it also tends to come to stalemates when no one is willing to move while the others are around. Like so:
Or like this:
Google the Hungarian name for more images.
Try it. It's fun.