What mystery number has 8 digits; none of the digits are the same. It is evenly divisible by 10. The value of one of the digits is 80,000. The digits in the millions place is the largest 1-digit odd number. The digit in the thousands place is 3 less than the digit in the millions place. The digit in the hundreds place is half the digit in the thousnds place. The digit in the tens place is 2 more than the digit in the ones place. The digit in the hundred thousands place is the largest single-digit factor of 25. The digit in the ten millions place is an even number. What is the mystery number?
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- evenly divisible by 10 -- the unit digit must be 0
- The digits in the millions place is the largest 1-digit odd number -- the second digit from the left must be a 9
- The digit in the thousands place is 3 less than the digit in the millions place --- it must be a 6
keep going this way.
To find the mystery number, let's break down the given information and use it to determine each digit.
1. The number has 8 digits, and none of the digits are the same.
This means that we need to find distinct digits for each place value.
2. The number is evenly divisible by 10.
Since a number is divisible by 10 if the last digit is 0, we know that the mystery number ends with 0.
3. One of the digits is 80,000.
Since the digit in the hundred thousands place is the largest single-digit factor of 25, and we know that 5 is the largest single-digit factor of 25, the digit in the hundred thousands place is 5.
4. The digit in the millions place is the largest 1-digit odd number.
The largest 1-digit odd number is 9, so the digit in the millions place is 9.
5. The digit in the thousands place is 3 less than the digit in the millions place.
Since the digit in the millions place is 9, then the digit in the thousands place is 9 - 3, which equals 6.
6. The digit in the hundreds place is half the digit in the thousands place.
Since the digit in the thousands place is 6, then the digit in the hundreds place is 6 / 2, which equals 3.
7. The digit in the tens place is 2 more than the digit in the ones place.
Let's call the digit in the ones place "x." According to this condition, the digit in the tens place would be x + 2.
8. The digit in the ten millions place is an even number.
Since the ten millions place has not been mentioned in the given information, we can choose any even digit for this place.
So, let's summarize the digits we've found so far:
- Ten millions place: Any even digit (we'll use 2)
- Millions place: 9
- Hundred thousands place: 5
- Ten thousands place: Not determined yet
- Thousands place: 6
- Hundreds place: 3
- Tens place: Not determined yet
- Ones place: Not determined yet
- Units place: 0 (since the number is divisible by 10)
Now, we need to find the remaining digits. To do this, let's work with the given conditions.
From condition 7, we know that the digit in the tens place is 2 more than the digit in the ones place, which we called "x." So, the digit in the tens place is x + 2.
The digit in the tens place cannot be greater than 9, so we can assume x + 2 ≤ 9, which means x ≤ 7.
Now, let's find the digit in the ten thousands place. Since the number is divisible by 10, the digit in the ten thousands place must be 0.
Finally, we can determine the digit in the ones place by considering all the conditions:
- The digit in the hundreds place (3) is half the digit in the thousands place (6), and half of 6 is 3.
- The digit in the tens place is 2 more than the digit in the ones place (x + 2).
So, the digit in the ones place is 3 - 2, which is 1.
Now that we have all the digits, let's put them together to find the mystery number:
Mystery number: 29,365,210
To find the mystery number, let's break down the given information step-by-step:
1. The mystery number has 8 digits and is evenly divisible by 10. This means its last digit must be 0.
2. One of the digits is 80,000, which means it must be in the ten millions place.
3. The digit in the millions place is the largest 1-digit odd number, which is 9.
4. The digit in the thousands place is 3 less than the digit in the millions place, so 9 - 3 = 6.
5. The digit in the hundreds place is half the digit in the thousands place, so 6 / 2 = 3.
6. The digit in the tens place is 2 more than the digit in the ones place. Since the digit in the ones place is 0, the digit in the tens place would be 2.
7. The digit in the hundred thousands place is the largest single-digit factor of 25, which is 5.
8. The digit in the ten millions place is an even number, and the only even number available is 8.
Putting all the digits together, the mystery number is: 89,563,020.