24*. The case of Brown, Jones, and Smith is being investigated. One of them committed a crime. During the investigation, each of them made two statements.

Brown: "I didn't do it. Jones didn't do it."

Smith: "I didn't do it. Brown did it."

Jones: "Brown didn't do it. Smith did it."

It was later found out that one of them told the truth twice, another lied twice, and the third told the truth once and lied once. Who committed the crime?
$\triangle$ The difficulty lies in the fact that we do not know who told the truth both times, who lied both times, and who lied only once. Let's consider three cases.

1) Suppose Brown told the truth both times.

Since, according to his statements, he and Jones did not commit the crime, the only one who could have committed it is Smith. Let's fill in the following table (Table 1).

We will place pluses only in the cells of the column corresponding to the criminal, and minuses in the other cells. We will use the letters "t" and "f" to the right of the pluses and minuses to indicate whether a given statement is true or false.

It turned out that not only Brown, but also Jones told the truth both times. But this contradicts the conditions of the problem.

2) Suppose Jones told the truth both times.

Let's construct the table (Table 2). Here, too, it turned out that both Jones and Brown told the truth both times.

3) Suppose now that Smith told the truth both times.

Let's fill in the table (Table 3). It turned out that this case is possible. Since this is the only such case, the criminal is Brown.

Answer: Brown.

Table 1

| Crime | B | J | S |
| :--- | :--- | :--- | :--- |
| Name |  |  |  |
| Brown | $-\text{t}$ | $-\text{t}$ | + |
| Jones | - |  | + +t |
| Smith |  |  |  |

Table 2

| Crime | B | J | S |
| :--- | :--- | :--- | :--- |
| Name |  |  |  |
| Brown | $-\text{t}$ | - t | + |
| Jones | - t |  | + + |
| Smith |  |  |  |

Table 3

| Crime | B | J | S |
| :--- | :---: | :---: | :---: |
| Name |  |  |  |
| Brown | $-\text{t}$ | $-\text{t}$ |  |
| Jones | + - |  | + + |
| Smith | $+\text{t}$ |  | $-\text{t}$ |