Write the number that matches the clues. My number has 2 hundreds. The tens digit is 9 more than the ones digit. My number is
The Correct Answer and Explanation is:
The number is 291.
Explanation
This numerical riddle requires logical deduction using place value and basic arithmetic. The problem provides two clues:
- The number has 2 hundreds, which indicates the hundreds digit is 2.
- The tens digit is 9 more than the ones digit.
To build the number, begin by fixing the hundreds digit. A digit of 2 in the hundreds place gives a base of 200. The next step involves identifying appropriate values for the tens and ones places that meet the second condition.
Let the ones digit be represented by a variable, say x. Then, according to the second clue, the tens digit must be x + 9. Digits in base-10 numbering systems range from 0 to 9. Therefore, x + 9 must also be less than or equal to 9, since the tens digit cannot exceed this range.
Solving the inequality:
- x + 9 ≤ 9
- Subtracting 9 from both sides gives: x ≤ 0
The only digit value that satisfies this condition is x = 0.
But this leads to a problem: if the ones digit is 0, then the tens digit becomes 9 (0 + 9), which is valid. The resulting number becomes 290.
However, another possible value is x = 1, giving a tens digit of 10, which is invalid since digits must range between 0 and 9. Thus, 0 is the maximum possible value for the ones digit under these constraints.
But now reverse the logic. Try assigning possible values to the ones digit starting from 0 and increasing, checking whether the corresponding tens digit (ones digit + 9) still falls within valid digit range (0–9).
Trying ones = 1 → tens = 10 → invalid
Trying ones = 2 → tens = 11 → invalid
Trying ones = 0 → tens = 9 → valid
So, the number becomes:
- Hundreds: 2
- Tens: 9
- Ones: 0
Final number: 290
Correction: Ones = 1, then tens = 10 (invalid)
Ones = 2, then tens = 11 (invalid)
Try ones = 1, then tens = 10 (invalid)
Only ones = 0, tens = 9 gives valid number: 290
Answer: 290
