Answer:
Stage 1: The greatest 7-digit number with no digit repeating would be 9,876,543. Unfortunately, while this number IS divisible by 11, it is not EVENLY divisible by 11 which is what I assume the OP wanted, but did not really specify.
Now, we can take that biggest number and add 4 to it to get 9,876,548 which IS divisible by 11 with no remainder, but now we don’t have 7 distinct digits because the 8 repeats. But, all is not lost because this gives us a starting point. We proceed by subtracting 11 successively as shown below:
9,876,548 - 11 = 9,876,537 Again, divisible by 11, but with a repeating digit.
9,876,537 - 11 = 9,876,526 Again, divisible by 11, but with a repeating digit.
9,876,526 - 11 = 9,876,515 Again, divisible by 11, but with a repeating digit.
9,876,515 - 11 = 9,876,504 And now we have a number that meets the criteria as it is evenly divisible by 11 and no digit repeats within the number.
Step-by-step explanation:
