Move a match to make the equation hold. This is a very common and interesting math problem. It seems that this kind of question can only be tried blindly. Maybe try it right. If you always try incorrectly, you will feel dizzy and choose to give up. In fact, there is a general solution to this problem. This method can also be tried, but all possible moves should be tried in an orderly way. The reason that random trial-and-error method can't be solved sometimes is that random trial-and-error will inevitably lead to repeated trial-and-error and some situations are omitted-it is certainly not easy to find the right test point. If you try all the movements in an orderly way, if the topic is correct, you can find the correct movement-this is the power of the exhaustive method.

The general solution to the problem of moving matches to make the equation hold is to list every possible moving situation. Next, how to list the cases of moving matches in an orderly manner is described in detail.

Give an example of a topic:

The above figure 0-8= 1 1 obviously does not hold. A match must be moved to make the equation valid.

Step 1- Decompose all components of the formula, including numbers and symbols;

The second step-choose which match of the object: the number and operation symbol of the whole expression are composed of n (n >; = 1), then the movement matching can come from any object in the formula. In this example, 1 matches can be removed from these six objects. There are many possibilities for n> to choose a match to move an object composed of 1 matches. For example, 8 can move its own different one and become 960;

Step 3- Where are the selected matches moved? The selected match can be moved to "1". Its source is its own object-causing its own object to change shape "2. Move to another object 3. Move to a blank position and become an operator such as a minus sign;

Step 1- Select a movement match+a movement position for each component of the formula in turn until the movement holding the formula is found;

A little abstract, let's take 0-8= 1 1 as an example to describe the above exhaustive method of moving matches.

The decomposed object is 0-8 =11;

Test the movement matching of these six objects in turn.

"0": 0' s own motion can become 9 or 6, and "9-8 = 1" and "6-8 =-2" are not valid; 0 moves to a position other than itself, and after taking a match from 0, it is obvious that 0 becomes a non-numeric incorrect;

-:-There is nothing to move by itself. If you move to the non-ego, there may be "moving to 0 makes the equation from 0 to 8 become 88= 1 1 untenable", "moving to 8", "moving to = not moving", "moving to1having 7 1 or 6544.

"8": 8 is not automatic, and non-automatic can be "8 to 6,8-6 =11,0+6 = 165438, 0-6 = 7 1, 0-6 =/kloc-0. 0+9 = 1 1, 0-9 = 7 1, 0-9 = 17, 0-9 = 1+0 is invalid. 8 becomes 0,8-0 =1.

Now that we have found the movement of the object "8", we can stop the movement experiment of the remaining objects;

In the formula, the motion of objects is divided into self-motion and non-self motion. 1234567890+- These objects all have their own corresponding motion laws, which are analyzed one by one as follows:

1 Don't move or move by yourself, because these will make 1 a legal object (non-numbers and symbols), and you can turn it into 7 by adding a match;

2. Automatic can be changed to 3. You can't move matches anywhere without self-exercise. Otherwise, the remaining matches are illegal and you cannot add matches.

3 can be replaced by 2 and 5, nothing more than self-help, adding a match can be replaced by 9;

4 no automatic and non-automatic matches;

5. Moving by yourself can be changed into 3, and adding a match can be changed into 9 and 6.

6 can be changed into 0 and 9 automatically, 5 if it is not automatic, and 8 if you add a match;

7 Self-movement without self-movement can be changed into 1, and adding a match can be changed into 2;