On the same calendar, the sum of four numbers circled by a square is 76. What's the date of these four days?

There are two rooms a and B. There are three switches in house a and three light bulbs in house B. house a can't see house B. each switch in house a controls a light bulb in the house. How can we stay in house a and house B once and know which switch controls which light bulb?
The answers are as follows:
First, turn on two switches in room a and turn off one in five minutes
Then go to room B. the one that's on is the one that's on in room a. the other two can be judged by the heat and cold of the light bulb

Can you circle a square in the calendar so that the sum of the four numbers in the square is 78? If so, what are the dates of these four days? If not, please give reasons

Suppose we can find such a square, the number in the upper left corner is x, then the other three numbers should be x + 1, x + 7, x + 8; then we should have: x + X + 1 + X + 7 + X + 8 = 78, that is: 4x = 62, the solution is: x = 15.5, the calendar can't have a decimal part, so the assumption is not true, we can't find such a square, so we can't circle such a square

Circle 2 * 2 numbers on the calendar with a square frame. If the sum of these four numbers is 76, please answer the following questions:
(1) What are the four numbers?
(2) Can the sum of four numbers be 66? 112? Please explain why

(1) Let a number be x, then the right one is x + 1, the next one is x + 7, and the other is x + 8x + (x + 1) + (x + 7) + (x + 8) = 764x + 16 = 76x = 15, then the four numbers are: 15, 16, 22, 23 (2) from (1), these four numbers can be expressed as 4x + 16. When 4x + 16 = 66, x = 12.5 is not an integer

The sum of 2 ≛ 2 numbers circled in a square on the calendar of a certain month is 64. What are the dates of these four days?

In a monthly calendar, each line represents a week, with seven days between the top and bottom
Let the first day be a
Then a + (a + 1) + (a + 7) + (a + 7 + 1) = 64
4a=48
a=12
12 13 19 20

On the same calendar, the sum of four numbers circled by a square is 76. What's the date of these four days?