[{description:"This has 3 arrays and must pass",alpha:[],beta:[1,1,1],gamma:[],delta:[1,1],epsilon:[1],zeta:[]},{description:"This has 2 non-empty arrays and must not pass",alpha:[],beta:[],gamma:[],delta:[1,1],epsilon:[1],zeta:[]},]

db.collection.aggregate([{"$match":{"$expr":{"$gte":[{$sum:[{"$cond":{"if":{$eq:["$alpha",[]]},"then":0,"else":1}},{"$cond":{"if":{$eq:["$beta",[]]},"then":0,"else":1}},{"$cond":{"if":{$eq:["$gamma",[]]},"then":0,"else":1}},{"$cond":{"if":{$eq:["$delta",[]]},"then":0,"else":1}},{"$cond":{"if":{$eq:["$epsilon",[]]},"then":0,"else":1}},{"$cond":{"if":{$eq:["$zeta",[]]},"then":0,"else":1}}]},3]}}}])