What is the largest odd number less than 500000 that can be formed using each of the digits 5 6 0 1 3 and 9 only once?

Answer 1

396501

We know that the digits in a number signify a higher value the further to the left they are in the number. Therefore we want to order the number in such a way so that we have the highest numbers toward the left, but we also have to ensure all the conditions are met.

Let's write down our numbers in descending order: 9,6,5,3,1,0.

The number has to be less than 500,000 so we can't start with the 9,6 or 5 else we would break this condition. So let's start with the 3 and cross it off our list.

3.....

Leaving 9,6,5,1,0

Now we can put in the 9, 6, & 5.

3965..

Leaving only 1 & 0 remaining.

We'd like to put the 1 next, then finally the 0 to make the number larger, but we have to make the number odd so we must put an odd number at the end (all odd numbers must have an odd last digit)!

So the largest number which meets the conditions is:

396501.

Answer 2

12