You don't need 20. We ran three dishwasher loads for only eight people recently, with simple cooking. One at the start of preparations so it would be empty and

You don't need 20. We ran three dishwasher loads for only eight people recently, with simple cooking. One at the start of preparations so it would be empty and we'd avoid a queue of dirty pots in the kitchen, one when the dishwasher filled up during the evening, and another at the end. To my mind, four loads for 20 people sounds low.