Answers for i am a-digit number. My hundreds digit is triple my thousands digit. The number formed by my tens and ones digits is triple the number formed by my thousands and hundreds digits. No digit appears more than once. what number am i?
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To find the number that satisfies the given conditions, we need to go through the problem step by step.
Let's assume the thousands digit is "x," the hundreds digit is "3x," the tens digit is "y," and the ones digit is "z."
From the given conditions, we can deduce:
1. The number formed by the thousands and hundreds digits is 3 times the number formed by the tens and ones digits. This implies that 1000x + 100(3x) = 10y + z. Simplifying this equation, we get 1000x + 300x = 10y + z, which can be further simplified to 1300x = 10y + z.
2. The hundreds digit is triple the thousands digit. This implies that 3x = x * 3, which simplifies to 3x = 3x.
3. No digit appears more than once. This means that x, 3x, y, and z are all unique digits.
Considering condition 2, we can conclude that x can be any single-digit number since 3x will always be equal to 3x.
Now, let's substitute x = 1, which we will use as an example.
Using condition 1, we get:
1300(1) = 10y + z
1300 = 10y + z
To solve this equation, we can treat it as a system of equations by considering that z can only be 1-9 (since it cannot be equal to x). We will start by checking z = 1:
1300 = 10y + 1
1299 = 10y
y = 129.9
Since y needs to be a whole number, we can conclude that z cannot be 1. We repeat this process for z = 2, 3, 4, and so on, until we find a solution for y.
Continuing with z = 2, we get:
1300 = 10y + 2
1298 = 10y
y = 129.8
Again, y is not a whole number, so z = 2 is not a solution.
We continue this process until we find a whole number solution for y. After checking all the possibilities for z, we move on to x = 2 and repeat the same steps. We continue this process until we find a valid solution where y is a whole number.
Once we find a valid solution for x, y, and z, we can construct the number using the values we found.
Note: It is important to mention that there may be multiple solutions, and you may need to check different values for x to find all of them.