Smartphone Puzzle: Can You Determine the PIN From a Math Equation?

Smartphone conundrum

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Losing your smartphone’s security code can be quite frustrating. But some people, like Leonard in this story, use mnemonic devices to remember their codes. Even with this trick, Leonard is struggling to recall his PIN. Can you help him out?

The Smartphone Puzzle

Leonard’s smartphone PIN is a perfect square. If you subtract one from its square root, the result is 85 less than the original number. With this information, can you figure out Leonard’s PIN using a math equation?

Solving the Puzzle

To find the solution, we need to recall some fundamental math principles, especially the following formula: (a−b)2=a2−2ab+b2(a – b)^2 = a^2 – 2ab + b^2(a−b)2=a2−2ab+b2.

Let’s denote xxx as the square root of Leonard’s PIN. Using the given information, we can set up the following equation:(x−1)2=x2−85(x – 1)^2 = x^2 – 85(x−1)2=x2−85

Next, we solve for xxx by manipulating the equation step by step:x2−(x−1)2=85x^2 – (x – 1)^2 = 85×2−(x−1)2=85

Expanding the equation, we get:x2−(x2−2x+1)=85x^2 – (x^2 – 2x + 1) = 85×2−(x2−2x+1)=85

Simplifying further:85=2x−185 = 2x – 185=2x−1

Adding 1 to both sides:86=2×86 = 2×86=2x

Dividing by 2:x=43x = 43x=43

So, Leonard’s PIN is 43243^2432. Calculating 43×4343 \times 4343×43:432=184943^2 = 1849432=1849

Leonard’s smartphone security code is 1849.

Why Solving Puzzles Is Beneficial

Engaging in puzzles like this isn’t just a fun way to pass the time; it’s also a great way to keep your mind sharp. Puzzles require logical thinking and problem-solving skills, which are valuable in many aspects of life.

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Did You Know?

The word “puzzle” comes from the Latin word “aenigma,” which means something hidden. One of the most famous ancient puzzles is the riddle of the Sphinx.

If you enjoyed solving this mathematical puzzle, try more on our website! Keep challenging yourself and sharpening your skills. Who knows what other intriguing puzzles you might solve next?

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