It was Saturday on 12 December, 1342. What was the day on 24 August, 1342?

Count the days from 24 August to 12 December within 1342: 7 (rest of August) + 30 (Sep) + 31 (Oct) + 30 (Nov) + 12 (Dec) = 110 days. 110 divided by 7 leaves a remainder of 5, so 12 December falls 5 weekdays ahead of 24 August. Working back 5 days from Saturday gives Monday.