The Four Digit Number Puzzle | Logic game for adults and kids with its answer

 

The Four Digit Number Puzzle

Question :

You have to find a four-digit number that meets the following criteria:

1. The number is greater than 999.
2. The first digit is three times the second digit.
3. The third digit is half the first digit.
4. The fourth digit is equal to the sum of the second and third digits.

Can you find the number?

Solution:

Let's break down the criteria:

1. The number is greater than 999: This means the number must be between 1000 and 9999.

2. The first digit is three times the second digit: Let's represent the first digit as $𝑎$ and the second digit as $𝑏$. So, $𝑎=3𝑏$.

3. The third digit is half the first digit: The third digit is $\frac{𝑎}{2}$.

4. The fourth digit is equal to the sum of the second and third digits: The fourth digit is $𝑏+\frac{𝑎}{2}$.

Now, let's find a number that satisfies all these conditions:

• From condition 1, the number must be greater than 999, so the first digit $𝑎$ must be at least 3. The second digit $𝑏$ can be any digit from 0 to 9.
• From condition 2, since $𝑎=3𝑏$, possible values for $𝑎$ are 3, 6, or 9. Let's try $𝑎=3$ and $𝑏=1$. Then $𝑎=3\times 1=3$, which fits condition 2.
• From condition 3, the third digit is $\frac{𝑎}{2}=\frac{3}{2}=1.5$. Since the digits must be integers, let's round it down to 1.
• From condition 4, the fourth digit is $𝑏+\frac{𝑎}{2}=1+\frac{3}{2}=1+1.5=2.5$. Again, rounding down to the nearest integer gives 2.

So, the four-digit number that meets all the criteria is 3162.