Number Operation Logic Puzzle

Hi Ramal, let's solve this logical operations problem together. We need to find the rule behind the symbol to determine the value of the final expression.

Let's look at the given equations. Fifty-three gives eighteen, forty-two gives eighteen, and sixty-four also gives eighteen. We need to find what fifty-two results in.

A common strategy in these puzzles is to look at the digits. Let's try multiplying the digits of each number and then adding something.

For fifty-three, five times three is fifteen. To get to eighteen, we need to add three. Notice that three is the second digit.

Let's check if this rule, a times b plus b, works for the next row. For forty-two, four times two is eight. If we add the second digit, two, we get ten. That doesn't match eighteen.

Let's try a different patterned approach involving squares. What if we square the first digit and add the second? Five squared is twenty-five, plus three is twenty-eight. Still not eighteen.

Let's try squaring the digits and subtracting. Five squared is twenty-five, and three squared is nine. Twenty-five minus nine is sixteen. Close, but not quite.

Wait, let's look at the sums. Five plus three is eight. Four plus two is six. Six plus four is ten. No obvious pattern there. Let's try combining operations on digits.

Let's look at the first one again: fifty-three gives eighteen. What if we add the digits and then multiply by something? Five plus three is eight. Eight times something is eighteen? No.

Let's try another one. What if we multiply the sum of digits by the first digit? For fifty-three: five plus three is eight, times five is forty. No.

Let's try this: the first digit cubed minus the second digit squared? Five cubed is one hundred twenty-five. Too large. Let's try the second digit raised to the power of the first? Three to the fifth power is too large as well.

Let's look at the results again. They are all eighteen. This is very specific. Let's try taking the product of the digits and adding something constant. Five times three is fifteen, plus three is eighteen. Four times two is eight, plus ten is eighteen. Six times four is twenty-four, minus six is eighteen.

Notice a pattern in what we are adding or subtracting? Three, ten, and negative six? Not quite. Let's try squaring the first digit and subtracting the second digit times some number. For five squared minus seven times three? twenty-five minus twenty-one is four. No.

Let's try this: five plus three is eight. Four plus two is six. Six plus four is ten. If we square the sum and adjust? eight squared is sixty-four. No.

Let's look at the digits again. What if we multiply the digits and add their sum? For 53: five times three is fifteen, plus five plus three is eight. Fifteen plus eight is twenty-three. No.

Let's try squaring the first and adding the second multiplied by something. Or simply, look at this pattern: five squared minus three times something. 25 - 7 = 18. 16 + 2 = 18. 36 - 18 = 18. Works! 5 squared minus 7, 4 squared plus 2, 6 squared minus 18. No.