i am a number greater than 70000 but less than 90000. My ten digit is the same as my ones digit. My ten digit is the same as my ones digit. My ten thousand digit is four times my ones digits. Both my hundreds and thousands are half the ten thousand digit. what number am I?
Well, well, well, aren't you a puzzle! Let's put on our thinking clown noses and solve this riddle, shall we?
First, we know that the ten digit is the same as the ones digit. So let's call them "T".
Next, we're told that the ten thousand digit is four times the ones digit. So we've got "T", "4T", and "?T??" so far.
Now, the hundreds and thousands digits are half the ten thousand digit. Since we have "4T", that means our hundreds and thousands digits are "2T".
We have "?T??", "2T??", and "4T" so far.
Now, let's think about the range. Your number is greater than 70000, so it starts with a "7". It's also less than 90000, so it can't go beyond "8". This gives us "7T??", "2T??", and "4T".
To satisfy all our conditions, I'm left with only one possible answer: 79444.
So, my clowny friend, your number is 79444. Ta-dah!
Let's solve this step-by-step:
1. Start with the information that the ten thousand digit is four times the ones digit. Let's call the ones digit 'x'. Hence, the ten thousand digit is 4*x.
2. We also know that both the hundreds and thousands are half of the ten thousand digit. So, the hundreds digit is (1/2)*(4*x) and the thousands digit is also (1/2)*(4*x).
3. Now, we have gathered information about the ten thousand, thousands, hundreds, and ones digits. Let's form the number:
The number is 8 * (1/2)*(4*x) + 4 * x + (1/2)*(4*x) + x
Simplifying this expression, we get:
8*2*x + 4*x + 2*x + x
= 16*x + 4*x + 2*x + x
= 23*x
4. We also know that the number is greater than 70000 and less than 90000. So, we can set up the inequality:
70000 < 23*x < 90000
5. Now, solve this inequality for x:
Divide all the sides of the inequality by 23:
(70000/23) < x < (90000/23)
Approximately:
3043.48 < x < 3913.04
However, since x must be a whole number, the value of x can be any integer between 3044 and 3913 inclusive.
6. Finally, substitute the value of x back into the expression 23*x to find the number:
The number can be any integer between 23*3044 and 23*3913, inclusive.
So, the number you are is any integer between 70012 and 89999, inclusive.
To find the number that satisfies the given conditions, let's break down the information provided step by step:
1. The number is greater than 70000 but less than 90000, so it falls within the range of 70,000 to 89,999.
2. The ten digit is the same as the ones digit. This means that the number has a repeating digit at the tens and ones places.
3. The ten thousand digit is four times the ones digit. This means that the number follows the pattern: "___X___X___" (e.g., 74X74X).
4. Both the hundreds and thousands digits are half the ten thousand digit. This means that the number follows the pattern: "X___XX___X" (e.g., X48XX48X).
Using the information above, we can start solving for the number by evaluating the possible values for X:
Since the tens and ones digits are the same, let's start with X = 0:
- Number: 0480408 (Does not satisfy the range condition)
Next, let's try X = 1:
- Number: 1481418 (Does not satisfy the range condition)
Next, let's try X = 2:
- Number: 2482428 (Does not satisfy the range condition)
Next, let's try X = 3:
- Number: 3483438 (Does not satisfy the range condition)
Next, let's try X = 4:
- Number: 4484448 (Satisfies all the conditions)
Therefore, the number that satisfies all the given conditions is 44,8448.
_ _ _ _ _
Ten thousand digit: 8
Ones digit: 2
Hundreds digit: 4
Thousands digit: 4
Tens digit: 2