The enigma of the life of Alexander the Great

The puzzles concerning ages can be particularly perverse, here is an example.

In a recent collection that we will not cite so as not to give a bad image of its author: " Yes Alexander The Great had died five years earlier, he would have reigned a quarter of his life. If he had lived nine more years, he would have reigned for half his life. Knowing that he died king, say how many years he reigned. "

To resolve this problem, the author notes the duration of the reign of Alexander and v the duration of his life before affirming that the information of the statement is written: r – 5 = V / 4 and r + 9 = v / 2. By subtracting the second equation at the first, he deduces r then v whence he concludes that Alexander the Great reigned 19 years and lived 56 years.

If it is indeed the historical figure who was king of Macedonia inantiquity, and conquered most of the known world of the time, this result is impossible because it is known that he died young. Indeed, a little research in history books gives July 21, 356 BC as the date of birth and June 11, 323 as date of death. Alexandre therefore lived 32 years, almost 33. On the other hand, he succeeded his father Philippe II after he was assassinated, in the summer of 336. Alexandre therefore reigned 12 or 13 years, depending on the exact date of his coming to power.

Question: Where is the error? In the enunciation of the enigma or in its solution?

Reply :

The statement corresponds to the known dates in the life of Alexander but the solution to the enigma is false.

More precisely, the equation of the problem is wrong because if Alexander had died five years earlier, his life would have lasted v – 5 and not v hence the first equation: r – 5 = (v – 5) / 4. Similarly in the second, v should be replaced with v + 9 which gives: r + 9 = (v + 9) / 2. By subtracting the first equation from the second, we get v = 33 which, carried in the first equation, gives r = 12. These two results correspond to history as it is known.

Find out more about Hervé Lehning

A normalien and an aggregator of mathematics, Hervé Lehning has taught his discipline for some forty years. Crazy about cryptography, a member of the Association of Reservists of the cipher and information security, he in particular broke the secrets of the encryption box of Henri II.

  • His blog MATH'MONDE on ABSMARTHEALTH

  • The Hervé Lehning's latest book :

Also to discover: The universe of secret codes from Antiquity to the Internet published in 2012 by Ixelles.

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