Question

there are 24 four-digit numbers which use each of the digits 1, 2, 3, 4. how many of these are divisible by 11

Answer 1

Answer:

1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, and 4321 are the 24 four-digit numbers that use 1, 2, 3, 4. Out of all these 24 four-digit numbers only the numbers: 1243, 1342, 2134, 2431, 3124, 3421, 4213, 4312 are divisible by 11.

Step-by-step explanation:

Answer 2

Answer:

  8 numbers divisible by 11

Step-by-step explanation:

The divisibility rule for 11 says that the difference between the sums of alternate digits will be divisible by 11 if the number is divisible by 11.

Here, the 4-digit number will be divided into two sums of 2 digits each when we apply that rule. Those two digits cannot have a sum greater than 7, so the only way for the number to be divisible by 11 is for alternate digits to sum to 5, so the difference of the sums is zero. That is, alternate digits must be {1, 4} or {2, 3}.

Those digits can appear in either order (1..4 or 4..1, for example), and either pair can have its first digit first (2 choices). That means, the 4 digits can be arranged in 2×2×2 = 8 ways to make a number divisible by 11.

Smallest to largest, the numbers are ...

• 1243
• 1342
• 2134
• 2431
• 3124
• 3421
• 4213
• 4312