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The Beautiful Princess

2023-10-31 |    0

In a distant kingdom, there resided a beautiful princess named Elizabeth, who harbored the dream of finding the wealthiest groom to share her life with. News of her quest spread like wildfire, and soon, a long line of eager suitors, numbering a thousand in total, formed outside the grand castle where the princess dwelled. However, the king, her father, was deeply concerned about her safety. To protect his beloved daughter, he issued a royal decree forbidding her from descending to meet the suitors en masse.

Princess Elizabeth, bound by her father's edict, was faced with a puzzling dilemma. She had to receive each suitor individually in her chambers on the castle's 10th floor. Naturally, she sought a method to select the richest groom. The princess reasoned that she couldn't marry the very first suitor, fearing that richer contenders might be further down the line. Yet, she also hesitated to marry the last suitor, thinking that the wealthiest groom might have been passed over by then.

Perplexed by this problem, the princess sought the counsel of the kingdom's esteemed court wizard, Merlin Berezovsky. Merlin was known for his mystical insights and profound knowledge. Upon hearing Elizabeth's predicament, he introduced her to a fascinating concept – Euler's magic number, denoted as e, which is approximately 2.71.

Merlin explained a clever strategy based on this magical number. He shared that if she interviewed the first 1000/2.71 suitors (approximately 369 of them) and then selected the first suitor who proved wealthier than all those 369 preceding ones, she would have a very high probability of choosing the richest one, approximately 63.1%.

Initially skeptical, the princess watched as Merlin worked his mystical powers on a modern contraption known as a laptop. With great precision, he programmed a small Python script and conducted a computer experiment using the Monte Carlo method. The results were astonishing and incontrovertible – the chances of selecting the wealthiest groom using this method were indeed approximately 63.1%.

With newfound confidence in Merlin's wisdom and modern magic, the princess embraced this innovative approach. She promptly interviewed the first 369 suitors and, as the fates would have it, married the first suitor who surpassed all his predecessors in wealth.

In the end, Princess Elizabeth's choice was guided by a blend of tradition and modernity, with a touch of mathematical elegance, all thanks to the enchanting insight of the court wizard Merlin Berezovsky and Euler’s magic number e.

You can find proof of Merlin's enchanting insight in the publication by S. M. Gusein-Zade, entitled "The Problem of Choice and the Optimal Stopping Rule for a Sequence of Independent Trials." Theory of Probability & Its Applications, 1965, Volume 11, Number 3, pp. 472–476.