Puzzle: What is the largest integer whose digits are all different (and do not include 0) that is divisible by each of its individual digits?
I am not proud of the process, but I at least have a big number to suggest as a candidate.
Clearly, I want as many digits as possible.
I want big digits to the left.
If it has many digits, some must be even, which means the number is even.
I throw out 5 because an even number divisible by 5 has 0 as LSD.
Also, it has to end in 5 if it contains 5 as a digit.
If it has 9, the sum of the digits is divisible by 9. The smallest digit I can throw out (besides 5, which is gone already) is 4.
I am tired already but I am working with 9,8,7,6,3,1,2.
I played a bit in Excel with swapping pairs of digits.
9867312 works.
Is that the largest possibility?
Too much thinking for a tired brain and too much sausage-making already.
So, I offer 9867312.
