# Thread: Finding the largest 4-digit integer

1. ## Finding the largest 4-digit integer

What is the greatest four-digit integer that meets the following three restrictions?

1. All of the digits are different.
2. The greatest digit is the sum of the other three digits.
3. The product of the four digits is divisible by 10 (no remainder) and not equal to zero.

2. Best I can do is

3. You have it correct. Did you try trial&error, logic or algebra or some combination? Just curious.

4. Just logic, really. The only way of getting something divisible by 10 is to have the product digits being 2 and 5 - no others will work. Since all the digits must be different, then the other one had to be 1, thus the largest must be the sum of these, 8. If you had 9, the 'other' digit would then have had to be 2 - and we have used 2 already...

I'm not any good at puzzles!

5. BATcher -You are a Genius .

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