Received answer to the following question from Jishka. (2469)
Would you please explain the steps you used to get the answer 2469. I must show work.
Using the 9 digits, 1, 2, 3, 4, 5, 6,7, 8 and 9 you can arrange four different digits to form a four-digit number that is NOT divisible by 7. The digits 1238 cannot be arranged to create a four-digit number that is divisible by 7. The digits 1389 also cannot be arranged to form a four-digit number that is divisible by 7. Find one additional set (not 1238 or 1389) of four different digits that is not divisible by 7. Provide the digits to form the smallest four digit value.
I could think of no easy way to determine the answer. I'd be interested to know what the teacher says as far as finding the solution quickly. I think that questions like this are a waste of time, because there's no real mathematical insight to be gained. It's just a matter of searching for something in a long list.
To that end, I wrote a small perl program that just tried all the 4-digit numbers. That was the only solution found.
Now, if they had wanted divisibility by 3 or 9, then you could use the casting out nines, which says that if the sum of the digits is divisible by 9, so is the number. Even that gives little help in reducing the list.
Unfortunately, casting out sevens requires factoring the number, so it doesn't help much. If any of the factors is divisible, then so is the number. (duh)
So, another way might be to check all numbers that contain only prime factors not including 7: 2,3,5,11,13,... but that's also tedious.posted by Steve