I am 5 digit number between 20,000 and 40,000. My ten thousand digit is 6 less than in ones digit and my thousands digit is more than my tens digit. My hundred digit is the sum of my ten thousands digit. What number am I?
between 20,000 and 40,000
2xxxx
3xxxx
4xxxx
mumble mumble
My hundred digit is the sum of my ten thousands digit.
???
To find the 5-digit number that meets the given conditions, let's go step by step:
1. The ten thousand digit is 6 less than the ones digit:
This means the ones digit could be any number from 0 to 9, and the ten thousand digit is always 6 less than that. Let's go through the possibilities:
- If the ones digit is 0, then the ten thousand digit would be -6, which is not possible for a digit.
- If the ones digit is 1, then the ten thousand digit would be -5, which is also not possible.
- If the ones digit is 2, then the ten thousand digit would be -4, still not possible.
- If the ones digit is 3, then the ten thousand digit would be -3, which is not possible either.
- If the ones digit is 4, then the ten thousand digit would be -2, still not valid.
- If the ones digit is 5, then the ten thousand digit would be -1, which is not a valid digit.
- If the ones digit is 6, then the ten thousand digit would be 0. This is a possible combination.
So, we have found that the ones digit is 6 and the ten thousand digit is 0.
2. The thousands digit is more than the tens digit:
Since the thousands digit is greater than the tens digit, it can be any number from 7 to 9. Let's go through the possibilities again:
- If the thousands digit is 7, then the tens digit would be 6, which is not possible.
- If the thousands digit is 8, then the tens digit would be 7. This is a possible combination.
- If the thousands digit is 9, then the tens digit would be 8, which is also a valid combination.
So, we have found that the thousands digit is either 8 or 9, and the tens digit is 7.
3. The hundred digit is the sum of the ten thousand digit:
Since the hundred digit is the sum of the ten thousand digit, we add 0 to the previous possibilities:
- If the thousands digit is 8 and the ten thousand digit is 0, then the hundred digit would be 0 + 8 = 8. This is a possible combination.
- If the thousands digit is 9 and the ten thousand digit is 0, then the hundred digit would be 0 + 9 = 9. This is also a valid combination.
Putting all the digits together, we have:
- If the thousands digit is 8, the ten thousand digit is 0, the hundred digit is 8, the tens digit is 7, and the ones digit is 6, the number would be 80,786.
- If the thousands digit is 9, the ten thousand digit is 0, the hundred digit is 9, the tens digit is 7, and the ones digit is 6, the number would be 90,796.
Therefore, there are two possible numbers: 80,786 and 90,796.