The world is overflowing with questions that have no answers.

While scrolling through social media, a math puzzle suddenly caught my eye.

It's the type of problem you often see floating around on timelines.

If you solve it normally, using simultaneous equations is the standard way.

Add the top and bottom equations to get 2x = 70, derive x = 35, then subtract to get y = 15.

And finally, 35 × 15 = 525.

It's the most reliable route, and a familiar one that everyone learns in school.

However, the moment I saw this problem, another route popped into my head.

"Couldn't I just square both sides and subtract them?"

If you subtract the squares of each (50^2 = 2500, 20^2 = 400), x^2 and y^2 cancel out perfectly, leaving only 4xy = 2100.

All that's left is to divide by 4. 2100 ÷ 4 = 525.
It's a method that accesses the 'xy' block I want to find directly, without having to reveal the individual identities of x and y one by one.

Today, starting from that small realization,"The reason why I love math"I'll write down a few thoughts about that.

◆ "Taking the long way"? "A shortcut"?

The difference in how to solve it. Isn't that really a difference in how one approaches a problem?

People who use simultaneous equations keep their feet on the ground and solve it step by step with certainty. It's a choice to 'proceed one step at a time,' a solid approach that won't collapse even with complex problems.

On the other hand, those who use algebraic identities to transform the equation choose to 'grasp it as a whole,' looking down at the overall structure and omitting unnecessary calculations.

Or perhaps there are people who intuitively assemble it in their heads as the distance from '25, which is the middle (average) of 50 and 20,' like elementary school sum-and-difference problems.

For them, the problem isn't just a task to get an answer. It's a 'puzzle of thought' to test their own weapons and intuition and to customize their solution method.

◆ The world of mathematics is always sincere

The world is overflowing with questions that have no answers.
Whichever you choose is correct, yet at the same time, a sense of unease remains. Compared to such a complex real world, the world of mathematics is always surprisingly sincere.

You can choose a solution method that feels like walking through a muddy road, or one that feels like smartly leaping through the air. After letting you fully enjoy the diversity of the thought process, in the end, it wraps everything up with a single, absolute truth—"525"the answer.

No matter what approach you take, as long as the logic holds, you will arrive at the same peak. I think that overwhelming tolerance and beauty are the reasons why I can't stop being attracted to it.

◆ You can decide the route to the correct answer yourself

"Which way of solving is the most correct?" There is no single answer to that question.

It's fine to enjoy the exhilaration of taking a shortcut in search of efficiency.

It's also fine to enjoy the sense of accomplishment of honestly repeating calculations and arriving at the answer with certainty.

What's important is your own sense of satisfaction regarding 'what process you went through to arrive at that answer,' isn't it?

If you have a question or a challenge in front of you right now that you want to solve,

please try tackling it with the 'route that feels most right' for you.

The pleasure of thinking with your own head, being creative, and arriving at that single answer will surely become a unique experience for you that nothing else can replace.

See you later 👋

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