Question

Кто прав? Учитель написал на доске четырехзначное число, в котором все цифры разные. Ученики по очереди сказали фразы: "данное число делится нацело на 3", "данное число содержит цифру 4", "данное число делится нацело на 6", "данное число содержит цифру 1 ". Известно, что один ученик сказал ложь, а трое сказали правду. Найдите наименьшее число из всех возможных, написанных учителем.​

Answer 1

Ответ:

1047

Пошаговое объяснение:

Answer 2

Ответ:

Ответ:

1074

вывод

1074  1248  1254  1284  1374  1428  1452  1458  1470  1476  1482  1524  1542  1548  1584  1674  1704  1734  1740  1746  1764  1794  1824  1842  1854  1974  2148  2154  2184  2418  2514  2814  3174  3714  4128  4152  4158  4170  4176  4182  4218  4512  4518  4710  4716  4812  5124  5142  5148  5184  5214  5412  5418  5814  6174  6714  7014  7104  7134  7140  7146  7164  7194  7314  7410  7416  7614  7914  8124  8142  8154  8214  8412  8514  9174  9714  

Answer 3

Finding the Smallest Possible Number

To find the smallest possible number that satisfies the given conditions, let's analyze the statements made by the students:

1. "The number is divisible by 3." 2. "The number contains the digit 4." 3. "The number is divisible by 6." 4. "The number contains the digit 1."

We know that one student lied and three students told the truth. Let's consider each statement and its implications:

1. If the number is divisible by 3, the sum of its digits must also be divisible by 3. This means that the sum of the digits must be either 3, 6, 9, 12, or 15. 2. If the number contains the digit 4, it can be any digit from 0 to 9 in the thousands, hundreds, tens, or units place. 3. If the number is divisible by 6, it must be divisible by both 2 and 3. Since it is already divisible by 3 (as per statement 1), it must also be divisible by 2. This means that the units digit must be an even number (0, 2, 4, 6, or 8). 4. If the number contains the digit 1, it can be any digit from 0 to 9 in the thousands, hundreds, tens, or units place.

Based on these conditions, we can start by considering the smallest possible number that satisfies the statements:

- The sum of the digits must be 3, so the smallest possible sum is 3. This means that the number must contain the digits 1 and 2. - The units digit must be even, so the smallest possible units digit is 2. - The number must contain the digit 4, so the smallest possible number is 124.

Now, let's check if this number satisfies the statements:

1. Divisible by 3: The sum of the digits (1 + 2 + 4) is 7, which is not divisible by 3. Therefore, this statement is false. 2. Contains the digit 4: The number 124 does contain the digit 4. Therefore, this statement is true. 3. Divisible by 6: The number 124 is not divisible by 6 because it is not divisible by 2. Therefore, this statement is false. 4. Contains the digit 1: The number 124 does contain the digit 1. Therefore, this statement is true.

Based on the analysis, we can conclude that the number 124 does not satisfy all the statements. We need to find a larger number that satisfies the conditions.

Let's consider the next smallest possible number:

- The sum of the digits must be 6, so the smallest possible sum is 6. This means that the number must contain the digits 1, 2, and 3. - The units digit must be even, so the smallest possible units digit is 2. - The number must contain the digit 4, so the smallest possible number is 1234.

Now, let's check if this number satisfies the statements:

1. Divisible by 3: The sum of the digits (1 + 2 + 3 + 4) is 10, which is not divisible by 3. Therefore, this statement is false. 2. Contains the digit 4: The number 1234 does contain the digit 4. Therefore, this statement is true. 3. Divisible by 6: The number 1234 is not divisible by 6 because it is not divisible by 2. Therefore, this statement is false. 4. Contains the digit 1: The number 1234 does contain the digit 1. Therefore, this statement is true.

Based on the analysis, we can conclude that the number 1234 does not satisfy all the statements. We need to find a larger number that satisfies the conditions.

Continuing this process, we can find the smallest possible number that satisfies all the statements.