It is less than 100,000.

It is an even number.

It is divisible by 2,3, and 6.

None of the digits is 30.

The digit in the hundreds place is two less than the digit in the thousands place.

The digit in the ten-thousands place is one more than the digit in the thousands place.

The digit in the tens place is one less than the digit in the hundreds place.

If the number were increased by 6, it would be divisible by 2,3,4, and 9.

The number would be ... ?

It is less than 100,000. - this means there are 5 digits

It is an even number. - this means the digit in the ones place is 0, 2, 4, 6, or 8

The digit in the ten-thousands place is one more than the digit in the thousands place. The digit in the hundreds place is two less than the digit in the thousands place. The digit in the tens place is one less than the digit in the hundreds place. - this means you have the following five options:

54,21x; 65,32x; 76,43x; 87,54x; 98,65x

None of the digits is 30. It is divisible by 2,3, and 6.

If the number were increased by 6, it would be divisible by 2,3,4, and 9.

--> I plugged in even numbers for the "x" and divided by 3, if the result was a whole number, then added 6 to the number and divided by 9. The first one I tried worked!

Answer: 54, 210