Losing your phone’s security code can be a real headache, especially if it’s a puzzle even to yourself! Let’s dive into a scenario where Léonard, despite using a mnemonic trick, can’t remember his pin code. Can you help him crack it using a math equation?
The Smartphone Puzzle
Léonard’s phone security code is a perfect square. If its square root were decreased by one, the code itself would decrease by 85. With these clues, can you find Léonard’s pin using a mathematical equation?
Solving the Smartphone Puzzle
To solve this, recall some basics about algebraic identities, specifically the formula: (�−�)2=�2−2��+�2(a−b)2=a2−2ab+b2.
Let’s denote �x as the square root of the code. The puzzle translates into this equation:
(�−1)2=�2−85(x−1)2=x2−85
By expanding and simplifying this equation, we can find the value of �x.
So, (�−1)2=�2−85(x−1)2=x2−85 becomes:
�2−2�+1=�2−85x2−2x+1=x2−85
This simplifies to:
�2−2�+1=�2−85x2−2x+1=x2−85
Subtract �2x2 from both sides:
−2�+1=−85−2x+1=−85
Add 85 to both sides:
−2�+86=0−2x+86=0
So,
2�=862x=86
Then,
�=43x=43
Thus, Léonard’s security code is 432432. Multiplying 43 by itself gives us:
43×43=184943×43=1849
The pin code for Léonard’s phone is 1849!
Conclusion
If you enjoyed cracking this mathematical puzzle, there are plenty more to challenge your brain on our site! Puzzles like this not only test your problem-solving skills but also keep your mind sharp.
Did you know? The word “puzzle” comes from the Latin “aenigma,” highlighting the importance of hidden meanings and clues. One of the oldest puzzles known is the famous riddle of the Sphinx.
Next time you’re stuck with a tricky code, remember, a little bit of math can go a long way!
Peter, a distinguished alumnus of a prominent journalism school in New Jersey, brings a rich tapestry of insights to ‘The Signal’. With a fervent passion for news, society, art, and television, Peter exemplifies the essence of a modern journalist. His keen eye for societal trends and a deep appreciation for the arts infuse his writing with a unique perspective. Peter’s journalistic prowess is evident in his ability to weave complex narratives into engaging stories. His work is not just informative but a journey through the multifaceted world of finance and societal dynamics, reflecting his commitment to excellence in journalism.
