SOLUTION: find the 5 digit number that has the following characteristics. -no 2 digits are the same. -no 0 occurs in the number. -the 3rd digit is 1 less than the 2nd digit. -the 2nd is

Question 9415: find the 5 digit number that has the following characteristics.
-no 2 digits are the same.
-no 0 occurs in the number.
-the 3rd digit is 1 less than the 2nd digit.
-the 2nd is twice the 1st digit.
-the sum of the 1st 4 digits is divisible by 9.
-the 4th digit is the square of the 5th digit.
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
Let's take the fact the second is double the first. This already rules out your choices for the second number. Since it's double the first, the second number has to be even. In this case, our number MAY only begin with 12, 24, 36, or 48.

Now, the third digit must be 1 less than the second digit. So then, we have to throw out the 12 for our choice because the number that is 1 less than 2 is 1, making our number begin with 121. We can't do that because we can't repeat a number we already had. We could say that the number so far is 243??, 365??, or 487??.

Let's throw in the fact that the 4th digit has to be the square of the 5th digit. The only "number and its square" duo that we can have are (3,9) and (4,2) where all are 1-digit numbers. That would force our number to end in a 93 or a 42. These two possibilities already rule out the 243?? choice because the 3 would be repeated if we had the 24393, and the 4 and 2 would be repeated when we say 24342.

With the 365??, though, we have to throw out the possibility 36593 because the 3 repeats. SO FAR, 36542 meets all the rules.

What about the 487?? ? We have to throw out the 48742 because the 4 repeats. We can have the 48793, though since no numbers doesn't repeat.

So far, we have narrowed it down to 2 choices - the 36542 and the 48793. We are now in the final round. Which one of these has the first 4 digits add up to a number divisible by 9? Let's check out the 48793. 4 + 8 + 7 + 9 = 28. That's not divisible by 9. We're left with the 36542. Could this be the winner then? 3 + 6 + 5 + 4 = 18. AHA! We found it. The sum of the first 4 digits is 18, which is divisible by 9.

36542 WINS!
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