There are 12 numbers on the clock face: 1, 2, 3, , 11, 12, a total of 12.

First of all, let me tell you, there is no skill in this topic at all, and then how to put it bluntly or make up.

First question. Because 1+2+3+......12=78。

So, all you have to do is make up a few numbers so that the sum of them is 39, and then add a negative sign to those numbers, or the rest of them.

Why is there no pattern, you see

12 + 11 + 10 + 6 (then of course, the remaining 9,8,7,5,4,3,2,1 is also a group.) )

12+11+9+7 group.

12+10+9+8 group.

11+10+9+8+1 and so on and so forth.

But 12 can be split into 3+9, 4+8, 5+7, so there is no rule to follow at all. In short, you can list as many groups as you want, and the only way to calculate the total number is to list them all. I believe that you will be given 1 hour, there is still hope to finish the list, be careful not to miss or repeat it...

That's why the person who came up with this question likes to play tricks).

Second question. (The meaning of the title should be to add a minus sign before all the numbers clamped by the hour and minute hands...) Otherwise, I don't know how many kinds. ）

For example, in the first question, it is sufficient to make the sum of consecutive numbers 39.

Then, to be consecutive, there are only 4, 5, 6, 7, 8, 9 and 12, 11, 10, 1, 2, 3 in this case

It's easy to see.

3, 4, 5, 6, 7, 8, 9 between 9:15 and 9:20

and between 3:45 a.m. and 3:50 a.m., 10, 11, 12, 1, 2, 3

Just add a negative sign to the front.

1) Try to prefix these numbers with positive and negative signs, so that their sum is exactly 0?

2) What mathematical rules can you summarize in the process of solving the problem?

Solution: Notice that (1-2) = (3-4) = (5-6) = (7-8) = (9-10) = (11-12) = -1;

So this problem translates to mark the positive or negative sign in front of the six -1s, so that their sum is 0, which is simple, as long as there are three positive and three negative can be satisfied, assuming that the first three are positive and the last three are negative, that is:

1-2) + (3-4) + (5-6) - (7-8) - (9-10) - (11-12), i.e.:

1-2+3-4+5-6-7+8-9+10-11+12, which is obviously 0.

The specific answer is:

Solution: 1) The symbols are: +1, -2, +3, -4, +5, -6, -7, +8, -9, +10, -11, +12;

2) In the problem solving, I found that the difference between each two adjacent numbers is -1, so just divide them into a group according to each two adjacent numbers, and add parentheses to make the difference, that is, (1-2), (3-4), (5-6), (7-8), (9-10), (11-12) After dividing into six groups, add 3 positive signs and 3 negative signs in front of these six groups, and then remove the parentheses, this problem is solved.

There are 12 numerals on the clock face, and the time it takes for the hour hand to travel over two adjacent numerals is 1 hour.

The process is as follows:

1) The intention of the clock dial is as follows:

2) The dial of a clock has 12 numbers on it, and these 12 numbers divide a circumference into 12 equal parts.

3) For the hour hand, the time to walk in one circle is 12 hours, then the time between two adjacent numbers is: 12 12 = 1 hour.

2 -3 4 -5 6 7 8 -9 -10 11 -12

2. No, because the original sum is 78, which is an even number, and changing any number to a negative number is equivalent to the sum minus twice the number, which must be an even number.

-1+2+3-4-5+6+7-8-9+10+11-12=0

Yes, 1+....12=13 6=78, any odd symbol can be changed.

Find 1, 2, 3, 4, 5 ,... first, 12 The sum of these 12 numbers is 78, and the sum of the absolute values of 5 negative numbers is 39 when 78 2 is obtained, and the sum of the absolute values of 5 numbers in the 12 numbers is equal to 39 in the book Tong Chonghong can be judged by adding a negative sign in front of the Hong

So there are: (1) 1+2+3+4+5+....+12 = 78,78 2 = 39,1 + 6 + 9 + 11 + 12 = 39, 5 numbers are 1, 6, 9, 11, 12 (the answer is not unique).

1) That is, five digits and a minus sign in front of 39.

a 4,6,7,10,12

b 5,6,7,9,12

c 3,6,7,11,12

d 3,6,8,10,12

2) The sum of the five numbers is 39

2) Rule: Add a negative sign in front of the sum of five numbers to 39.

Solution: (1) 1 2 3 5-4+6 7 8 9+10+11+12

2) Rule: Calculate the sum first, take half, add a positive sign before the sum of half of the number, and add a negative sign before the rest of the number.

-12+(-11)+(6)+(10)+1+2+3+4+5+7+8+9 -9+(-7)+(2)+(1)+(12)+(8)+3+4+5+6+11+10 -3+(-6)+(10)+(11)+(9)+1+2+4+5+7+8+12 This rule is to add up the numbers 1 to 12, and the sum is 78, and then divide by 2 to get 39. Then add several of the numbers from 1 to 12 to 39 so that the two parts are opposite to each other, and together they are equal to 0.

（1）1-2+3-4+5-6-7+8-9+10-11+12=0

2) Yes, 1+3+5+7+9+11=36,36 2=18,7+11=18,1+3+5+9=18

3) No, 2+4+6+8+10+12=42, and 42 2=21, even plus even cannot be called odd.

(1). 1-2+3-4+5-6-7+8-9+10-11+12=0

2).From (1), it can be seen that the law of adding negative signs is that three are added before the odd number and three are before the even number, so it cannot be established only if the sum is added before the odd number.

3).No, for the same reason.

Ideas:1Divided into 6 groups: 1+12 2+11 3+10 4+9 5+8 6+7

2.It was found that each group was 13, so the two fiber branches were subtracted, and the vertical answer was 0