24:15::32:?::46:26

Steps to Solve

1. Identify the relationship between 24 and 15

We need to find out how 15 is obtained from 24. One possible relationship is subtracting 9: $24 - 9 = 15$.

2. Identify the relationship between 46 and 26

Similarly, let's check if the same relationship exists between 46 and 26. $46 - 20 = 26$

3. Look for an alternative relationship between 24 and 15

Since simple subtraction doesn't yield a consistent pattern, let's explore another relationship. Consider multiplying the digits of the first number and subtracting that product from the first number: $24 \rightarrow 2 \times 4 = 8$, and $24 - 8 = 16$ This does not match to the 15.

Let's try something else. Consider multiplying the digits of the first number, and subtracting the product from first number by 1: $24 \rightarrow 2 \times 4 = 8$, and $24 - 8 -1 = 15$. $46 \rightarrow 4 \times 6 = 24$, and $46 - 24 -1 = 21$ This does not match to the 26.

Lets try an alternate relationship $24 \rightarrow 2 \times 4 = 8$. $15 = 24 - 8 -1$ $46 \rightarrow 4 \times 6 = 24$. $26 = 46 - 24 + 4$. This also seems to be a different pattern

4. Analyze the first relationship further: $24 - 15 = 9$ and $46 - 26 = 20$

Examine the difference between the numbers. The difference between 24 and 15 is 9. The difference between 46 and 26 is 20. Perhaps the digits are multiplied and squared, then that number is subtracted.

$24 : 15 \implies 24 - (2 + 4)^2/4 = 15/4 $ No $24 : 15 \implies 2x + 4x = 6x, then 15 = 24 - 9 , where 9 could relate to $x^2$ and x = .5

5. Trying another pattern

Consider multiplying the individual digits and adding to the original number.
$24 \implies 2 \times 4 = 8$, and $15 = 24 - 9$. $46 \implies 4 \times 6 = 24, and $26 = 46 - 20$ $32 \implies 3 \times 2 = 6, and 32 - X = ?$

$24 - 9 = 15, 46 - 20 = 26, 32 - ? = unknown$ We examine 9, 20 and ? relationship We see $9 = 3^2, 20 \approx 4.47^2$. The difference between 2, 4 and 3 is 1. So could try it out. $32 - (3 + 2 + 1^2+1) = $32 - 6^2/1$? 32: ? .

6. Focus on the differences and look for a pattern: $24 - 15 = 9 = 3^2$ $46 - 26 = 20$

If $24 - 15 = 9$, $46 - 26 = 20$. $\sqrt{9}$ is 3, $\sqrt{20}$ is approximately 4.47.

Pattern could be. $24: 15 => 24 - (2+1)^2 = 15$ $46:26 => 46 - (4+ \approx1.5)^2 = 26 $

Consider: $ first ; number - some ; expression = second ; number $

$(24+15)/2 = 19.5 => ~20$ is square root of 400. and then 400 / 64?

7. Last try: multiplying the ones and tens digit, then subtracting it from the first number and subtracting/adding a constant Trying out this pattern: $24: 15 => (24) = 8 => 24-8=16 ~ sub 1 => 15$ $46: 26 => (46) = 24 => 46-24=22 ~ add 4 => 26$ $32: ? => (3*2) = 6 => 32-6 = 26 "similar to the other numbers~ subtract 5? 26 - 5 = 21. Another route could be to add 5, 26 + 5=31.