A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or a multiple of 11.
Given the set of digits {0, 1, 2, 5, 7, 9}, let's consider the possible combinations of these digits to form 6-digit numbers.
**Case 1: The sum difference is 0 (0 mod 11):**
- The digits in odd positions must be the same as the digits in even positions.
- There are 3 odd positions and 3 even positions.
There are 3 possible digits for the odd positions ({0, 5, 9}) and 3 possible digits for the even positions ({0, 5, 9}). So, there are 3 * 3 = 9 combinations for this case.
**Case 2: The sum difference is a multiple of 11:**
- The digits in odd positions and even positions must differ.
There are 3 possible digits for the odd positions ({1, 2, 7}) and 3 possible digits for the even positions ({0, 5, 9}). So, there are 3 * 3 = 9 combinations for this case as well.
Therefore, the total number of 6-digit numbers from {0, 1, 2, 5, 7, 9} that are divisible by 11 is 9 (Case 1) + 9 (Case 2) = 18.
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A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or a multiple of 11.
Given the set of digits {0, 1, 2, 5, 7, 9}, let's consider the possible combinations of these digits to form 6-digit numbers.
**Case 1: The sum difference is 0 (0 mod 11):**
- The digits in odd positions must be the same as the digits in even positions.
- There are 3 odd positions and 3 even positions.
There are 3 possible digits for the odd positions ({0, 5, 9}) and 3 possible digits for the even positions ({0, 5, 9}). So, there are 3 * 3 = 9 combinations for this case.
**Case 2: The sum difference is a multiple of 11:**
- The digits in odd positions and even positions must differ.
There are 3 possible digits for the odd positions ({1, 2, 7}) and 3 possible digits for the even positions ({0, 5, 9}). So, there are 3 * 3 = 9 combinations for this case as well.
Therefore, the total number of 6-digit numbers from {0, 1, 2, 5, 7, 9} that are divisible by 11 is 9 (Case 1) + 9 (Case 2) = 18.