Behind a mathematical riddle often hides a more or less deep mathematical question, the question posed being a dressing. This is the case with first degree equations.
A father is 30 years older than his son, between them they are 36 years old, how old is the son?
These problems take their toll, they seem so simple that we forget to think about it: we trap ourselves and we answer wrong … We can pose the same problem under another label, for example by talking about a bottle and its cap.
A corked bottle
With its cap, a bottle weighs 110 grams. The bottle weighs 100 grams more than the cork. What is the weight of the cap?
Responnse
The answer regarding the son’s age is not six years old. Likewise, the weight of the cork is not 10 grams, otherwise the bottle would weigh 100 grams more, or 110 grams and the corked bottle 120 grams. This calculation false allows us to deduce that the cork weighs five grams. Likewise, the son is three years old.
We can find this result directly by algebra. Noting x the weight of the cap, that of the bottle is 100 + x so that of the corked bottle 100 + 2x = 110, which provides ” x “. The same equation solves both problems and many more. In fact, our two puzzles are a wrapping of the same question mathematical about the equations of the first degree.
Learn more about Hervé Lehning
Normalian and agrégé in mathematics, Hervé Lehning taught his discipline for more than forty years. Crazy about cryptography, member of the Association of Cipher and Information Security Reservists, he in particular unraveled the secrets of Henry II’s cipher box.
- His blog MATH’MONDE on Futura
- the last book by Hervé Lehning :
Also to discover: The universe of secret codes from Antiquity to the Internet published in 2012 by Ixelles.
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