My number has the same number of thousands as tens. It has three hundreds and no ones. The sum of its digits is 11
_ 3 _ 0
4,340
Oh, I hate math problems. They always make me feel divided! Anyway, let's solve this riddle, shall we?
Since your number has the same number of thousands as tens, that means it must be in the form 1X,1X,1X,0X0. (X represents any digit.)
You mentioned that it has three hundreds and no ones. So, the possible values for X could be 2, 3, 4, 5, 6, or 7.
Now, let's check the sum of the digits. If we add the X values, we need the sum to be 11.
If we choose X as 2, 3, 4, 5, 6, and 7, respectively, the sum of the digits would be:
2 + 2 + 2 + 0 + 3 + 0 = 9
3 + 3 + 3 + 0 + 4 + 0 = 13
4 + 4 + 4 + 0 + 5 + 0 = 17
5 + 5 + 5 + 0 + 6 + 0 = 21
6 + 6 + 6 + 0 + 7 + 0 = 25
7 + 7 + 7 + 0 + 8 + 0 = 29
None of these options gives us a sum of 11. Hmm, it seems like I've run out of numbers to be funny with. So, the only logical conclusion is that there is no solution to this problem. But hey, at least we had a good laugh, right?
Let's break down the information given step-by-step to find the number.
Step 1: "My number has the same number of thousands as tens."
This means that the thousands digit is the same as the tens digit.
Step 2: "It has three hundreds and no ones."
Based on this information, the hundreds digit is 3, and there are no ones, so the ones digit is 0.
Step 3: "The sum of its digits is 11."
Since there are no ones, and the thousands and tens digits are the same, we can conclude that the sum of the hundreds, thousands, and tens digits should be equal to 11.
From steps 1 and 2, we know that the hundreds digit is 3 and the ones digit is 0. So, the sum of the hundreds, thousands, and tens digits must equal 11 - (3 + 0) = 8.
To have a sum of 8, the thousands and tens digits must add up to 8. The possible combinations are:
- 8 + 0
- 7 + 1
- 6 + 2
- 5 + 3
- 4 + 4
However, we know that the thousands and tens digits are equal. Therefore, the only possible option is 4 + 4.
So, the number is 4,440.
To find the number with the given conditions, we can use a systematic approach.
Let's break down the information provided:
1. The number has the same number of thousands as tens.
Let's call this common digit "x."
2. The number has three hundreds.
This means the hundreds digit is 3.
3. The number has no ones.
This means the ones digit is 0.
4. The sum of its digits is 11.
Let's use this information to find the value of the remaining digit(s).
Now, let's determine the value of "x" using the first condition. Since the thousands digit is "x" and the tens digit is "x" as well, we can represent the number as "3x0x."
Next, we need to figure out the value of "x" using the fourth condition, which states that the sum of the digits is 11. From our number representation "3x0x," we can write the equation:
3 + x + 0 + x = 11.
Simplifying the equation, we get:
2x + 3 = 11,
2x = 11 - 3,
2x = 8,
x = 4.
Now that we know x = 4, we can substitute it back into the original number representation "3x0x":
3004.
Therefore, the number that satisfies all the given conditions is 3004, where the thousands and tens digits are both 4, the hundreds digit is 3, and the ones digit is 0.