use the clues to find the 7th digit mystery number.
* it is between 7 and 8 million
* it contains all of the digits greater than 1 and less than 8
* the hundred thousands digit is 3
* the ten thousands digit and the thousand digits are the same
* the tens digit is greater than the hundreds digit.
Using the first and third clues, the number is 7,3xx,xxx. From the second clue, the remaining numbers are 6, 5, 4, 2, with one of them being repeated (fourth clue).
However, I cannot find a definitive way of placing the the remaining four numerals. Several arrangements could fit, for example:
7,366,245
7,355,462
7,344,256
Have you omitted some information?
I hope this helps. Thanks for asking.
7,344,256
Let's break down the given clues to find the 7th digit of the mystery number:
1. The number is between 7 and 8 million.
- This means that the number is greater than 7,000,000 and less than 8,000,000.
2. The number contains all of the digits greater than 1 and less than 8.
- This means that the number contains the digits 2, 3, 4, 5, 6, and 7.
3. The hundred thousands digit is 3.
- This means that the digit in the hundred thousands place is 3.
4. The ten thousands digit and the thousand digits are the same.
- This means that the digit in the ten thousands place is the same as the digit in the thousands place.
5. The tens digit is greater than the hundreds digit.
- This means that the digit in the tens place is greater than the digit in the hundreds place.
Using these clues, let's start solving:
- The hundred thousands digit is 3, so the mystery number is in the range of 7,300,000 to 7,999,999.
- The ten thousands digit and the thousand digits are the same, so the mystery number must have a repeating digit in the ten thousands and thousands place.
- The tens digit is greater than the hundreds digit, so the mystery number cannot have a 3 in the hundreds place.
Now, let's try to find the exact digit in the ten thousands and thousands place based on the available digits (2, 4, 5, 6, and 7):
- Since the tens digit is greater than the hundreds digit, the only possible digits for the hundreds place are 2 and 4.
- Case 1: If the hundreds digit is 2:
- The available digits for the ten thousands and thousands place are 4, 5, 6, and 7.
- Let's try each possibility until we find the correct one:
- 742,xxx
- 745,544 (Not valid as it contains a repeating digit in the ten thousands and thousands place)
- 746,xxx
- The highest valid number in this case is 746,xxx.
- Case 2: If the hundreds digit is 4:
- The available digits for the ten thousands and thousands place are 2, 5, 6, and 7.
- Let's try each possibility until we find the correct one:
- 752,xxx
- 756,xxx
- 762,xxx
- 764,xxx
- The highest valid number in this case is 764,xxx.
Therefore, the 7th digit of the mystery number can either be x from 746,xxx or x from 764,xxx. Without additional information or a specific condition, we cannot determine the exact value of the 7th digit.
To find the 7th digit mystery number, let's break down the given clues:
Clue 1: It is between 7 and 8 million.
This means the number is greater than or equal to 7,000,000 and less than 8,000,000.
Clue 2: It contains all of the digits greater than 1 and less than 8.
This means the number must contain the digits 2, 3, 4, 5, 6, and 7.
Clue 3: The hundred thousands digit is 3.
This tells us that the number starts with 3 followed by six more digits.
Clue 4: The ten thousands digit and the thousands digit are the same.
This means the ten thousands digit is equal to the thousands digit.
Clue 5: The tens digit is greater than the hundreds digit.
This implies that the hundreds digit is smaller than the tens digit.
By combining these clues, we can start constructing the mystery number.
1. Since the hundred thousands digit is 3, we already have the first digit: 3.
2. We know the ten thousands digit and thousands digit are the same. So, let's assume they are both 4.
So far, we have the number as 34____.
3. The tens digit is greater than the hundreds digit.
The hundreds digit must be smaller, so it could be 2, and the tens digit could be 5.
Now, we have the number as 345___.
4. The remaining digits must include 2, 6, and 7, in any order.
Combining the clues, our mystery number can be any one of these possibilities:
- 345267
- 345726
- 346257
- 346725
- 347256
- 347625
One of these possibilities is the 7th digit mystery number!