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I'm sure when they arrived at the party with their son Sam they were given assurances by the Perry family - who would have been aware of his condition - "Don't worry, he'll be okay".
So you have an aspergers son, you go to a party. The hosts say "don't worry he'll be okay". As a parent do you think:
1) Oh great, they obviously know about aspergers and will take good care of him.
2) Yeah, thanks for the offer, but aspergers sufferers have issues with social interaction and it would be better if we stayed close by.
Also, the mother denies knowledge that she was told he was a sufferer.
If this was at a playschool or similar, anyone with a disability such as aspergers would have to have one on one supervision. The parents would know this but still left him supervised by just one adult.
Leaving all this aside, you are now saying that at a kids party, everyone needs to be supervised at all times. Since kids tend to run around this means that you would probably need around 3 or 4 adults for 10 kids. Obviously, they would have to have had lessons on how to control other people's children and be well versed as to what is and what isn't appropriate.
Risk assessments for every game should be done in advance eg if someone played football and a supervisor thought </> they were going in for a tackle, the game should immediately be stopped in case of injury. Also, if a shot was on target and going into the corner of a goal, the goalkeeper should be prevented from diving in case he were to hit his head on the post and cause brain damage.