There was no need to issue a challenge where we trained, as everybody fought everybody all the time. Want to try and test your mettle against one of the fighters, go right ahead.
With an open door policy sometimes an unknown outsider would come in looking to spar. They were always welcome. As for "challenging" someone, never really saw too much of that. Maybe a couple of times. Those people went down in the lore of "one time this fool came in..."
Think about it, if you're really a good Martial Arts fighter you don't go around issuing challenges. You don't have to. Because if you do, you become one of those stories.
Had a kid in Law Enforcement when I was teaching DT. After an eight hour block I was changing to go home. He walks up to my locker and throws a slow side kick up in front of my face, not trying to hit me, but to show off his flexibility. It was cute.
Long story short he wants to come to my dojo to do some sparring. I give him directions. He comes. He watches some sparring. But he doesn't want to spar with anyone but me. Okay. So we start to spar. Within thirty seconds I realize he has no fighting ability whatsoever, I mean, he's just awful. I do not wish to embarrass him, so I just move around, slapping away what he throws.
He suddenly takes an honest to God hissy fit. Starts screaming at me to "try and hit him". I'm kind of stunned, hadn't seen an adult brat in my dojo before. I try to talk to him - more hissy fit, even louder screaming. One of the black belts speaks up and says, "Coach, you always taught us to grant a guest his wishes." (I've learned just as much from my students as they've learned from me.)
From that moment on, I hit this boy with everything. Not hard, you could go to hell for that, just often. I was sweeping him, head kicking him, scissoring him, slapping him, spin kicking him, hitting him with things I didn't even throw anymore. And it's when the devil grabbed my soul and I started yelling at him, "You come in here and disrespect our dojo you M%#*//*^er!
He faked being dizzy from a backlist that wouldn't have broken an egg and stopped sparring.
I had to talk to my bosses at work the next day, let them know what we had in our midst. He was still on probation and was let go immediately. Next think we hear, not a month later, he married a hooker - who stole everything he had, including his car and bank account.
So one of the few times I've been challenged was by a foolish fruitcake. I'm not proud to be 3 and 0 against such fruitcakes. It's actually rather embarrassing.
I've become close friends with some of my black belts over the years. Some still tease me about it, saying, "he slapped around a mentally challenged kid one time. Next week he's going to fight a blind guy."