Will several XBEE transmitters work at the same time?

I’m making a system for judges in weightlifting who can give thumbs up or thumbs down after a lift by pressing one of two buttons. I had planned to keep an arduino with an xbee unit in each remote, and then one in the scoreboard for receiving.
However, I wonder is this possible if all judges give their score at the exact same time or will the receiving end have a hard time differentiating the messages from each other?
I figured if I let them all send something like a short text string identifying the remote and specifying the result.

I would not worry aboiut it as you are talking about the Juedges pressing a butten at the exact same microsecond in time for a data collosion to occur.

On a side note, why not just use the S1 modules with DIO line pasing on the Judges side and an arduino with an S1 in API mode on the Score board side. Then you can have the module simoply send a packet when a change is detected in the line. Reduces hardware and code. Also decreases complexity.

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Thanks for you answer! That sounds great.

I will have to look into the details of what you are suggesting as it is currently more or less unintelligible to me.
Do you mean it is possible to have an xbee transmitter working without an extra processor like an arduino to tell it what message to send? If so it definately sounds like a brilliant way to cut complexity and cost by a lot!
Thanks again.

Try reading over http://www.digi.com/support/kbase/kbaseresultdetl?id=2188.