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We know about Google Calendar, but it doesn't calculate compatible time slots for participants and probably force participants to use Gmail, which wouldn't work.
Ideally, participants could submit an order of preference. In other words:
1st Choice - Monday 1400-1600
2nd Choice - Wednesday 0900-1100
3rd Choice - Thursday -1200-1500
The site would assess all available mutually compatible time windows, and produce the results.
Thanks, XXXXX XXXXX I'll give it a go.