The number of visitors to a museum on five days was Monday 240, Tuesday 180, Wednesday 300, Thursday 210, Friday 270. On exactly one of these days the number of visitors equalled the mean of the other four days. Which day was it?

The five days total 1200 visitors. If a day's count d equals the mean of the other four then (1200 − d)/4 = d, so 1200 = 5d and d = 240 — in other words the day must sit exactly at the mean of ALL five days, 1200 ÷ 5 = 240. Monday's 240 is the only match, and the other four days do indeed average (1200 − 240)/4 = 240. Once you see that the day in question has to equal the overall mean, no day-by-day trial is needed.