What is the three digit mystery number? Clues:
It is less than 300, the tens digit is 4 more than the hundreds digit, the sum of the digits is 9, the hundreds digit is 2 less than the ones digit.
1 5 3
2 6 4
Which of those sets of digits adds up to 9?
A 2 in ten places The hundred digit 5 greater than the ten digit. The one digit 1 less than the hundred digit
Let's use the given clues to determine the three-digit mystery number step-by-step.
Clue 1: It is less than 300.
This means that the hundreds digit cannot be 3. Therefore, it can only be 1 or 2.
Clue 2: The tens digit is 4 more than the hundreds digit.
If the hundreds digit is 1, then the tens digit would be 1 + 4 = 5.
If the hundreds digit is 2, then the tens digit would be 2 + 4 = 6.
Clue 3: The sum of the digits is 9.
If the hundreds digit is 1 and the tens digit is 5, then the ones digit would be 9 - (1 + 5) = 3.
If the hundreds digit is 2 and the tens digit is 6, then the ones digit would be 9 - (2 + 6) = 1.
Clue 4: The hundreds digit is 2 less than the ones digit.
If the hundreds digit is 1 and the ones digit is 3, this is not satisfied.
If the hundreds digit is 2 and the ones digit is 1, this is satisfied.
Therefore, the three-digit mystery number is 216.
To find the three-digit mystery number, we can use the given clues one by one and narrow down the possibilities.
1. It is less than 300:
This tells us that the first digit (hundreds digit) of the mystery number can only be 1 or 2.
2. The tens digit is 4 more than the hundreds digit:
Let's consider the two possibilities for the hundreds digit:
For the hundreds digit as 1, the tens digit would be 1 + 4 = 5.
For the hundreds digit as 2, the tens digit would be 2 + 4 = 6.
3. The sum of the digits is 9:
Let's consider the two possibilities for the tens digit:
For the tens digit as 5, the ones digit will be 9 - (1 + 5) = 3.
For the tens digit as 6, the ones digit will be 9 - (2 + 6) = 1.
4. The hundreds digit is 2 less than the ones digit:
Let's consider the two possibilities for the ones digit:
For the ones digit as 3, the hundreds digit will be 3 - 2 = 1.
For the ones digit as 1, the hundreds digit will be 1 - 2 = -1. However, since the hundreds digit cannot be negative, this is not a valid option.
Therefore, the only valid solution is:
The mystery number is 156.