Archive for the ‘Puzzle’ Category

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Lesson 7: Solution to Diophantus Riddle (VI)

March 17, 2012

This is the translation of the epitaph into Spanish:

” Aquí fueron sepultados los restos de Diofanto. La infancia de Diofanto duró 1/6 de su vida, 1/12 en la adolescencia, cuando la barba cubrió su cara, Después de 1/7 de su vida contrajo nupcias. Luego de cinco años de casado nació su primer hijo. El hijo vivió ½ de la vida de su padre, su padre buscó consuelo en los números pero no lo logró y murió cuatro años después que él.”

Let x be the age of Diophantus. If we translate the epitaph into Algebra:

x/6 +x/12 +x/7 +5 +x/2 +4 = x
14x/84 +7x/84 +12x/84 +420/84 +42x/84 +336/84= 84x
14x +7x +12x +420 +42x +336= 84x
14x +7x +12x +42x -84x= -420 -336
-9x = -756
x = -756/-9 =  84  years old.

 

 
 
Then we have that Diophantus was born about 200 and died about 284.

Thanks  Lidia for your effort!

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Lesson 7: Linear and Quadratic Equations. Maths Are Magic (V)

March 5, 2012

How old are you? 

If you ask this to your great-aunt it would be indiscreet. So we are going to do it in other way …Play the following game

Tell her:Think of a number between 1 and 9.
Multiply it by 9.
Take away this result from 10 times your age and tell me the answer. 

Now you could guess your great-aunt’s age.

 

You will always get your great-aunt’s age. Is it Magic or Maths?

Why are we always right? Could you give a logic reason?

Freely translated from Matemágicas. Descartes Project
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Lesson 7: Who Was Diophantus? Diophantus’s Riddle (IV)

February 25, 2012

Diophantus of Alexandria

 

Born: about 200   Died: about 284

Diophantus is often known as the ‘father of algebra’,but there is no doubt that many of the methods for solving linear and quadratic equations go back to Babylonian mathematics. Nevertheless, his remarkable, collection of problems is a singular achievement that was not fully appreciated and further developed until much later.

 He is best known for his Arithmetica, a work on the solution of algebraic equations and on the theory of numbers. The Arithmetica is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. The method for solving the latter is now known as Diophantine analysis. Only six of the original 13 books were thought to have survived and it was also thought that the others must have been lost quite soon after they were written. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions.

 Diophantus did not use sophisticated algebraic notation, he did introduce an algebraic symbolism that used an abbreviation for the unknown and for the powers of the unknown.

 However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived.

You can read a good biography on

http://www.gap-system.org/~history/Biographies/Diophantus.html,

where I found this information. There are many biographies of famous mathematicians.

 Diophantus Riddle

 Much of our knowledge of the life of Diophantus is derived from a 5th century Greek anthology of number games and strategy puzzles. One of the problems (sometimes called his epitaph) states:

‘Here lies Diophantus,’ the wonder behold.

Through art algebraic, the stone tells how old:

‘God gave him his boyhood one-sixth of his life,

One twelfth more as youth while whiskers grew rife;

And then yet one-seventh ere marriage begun;

In five years there came a bouncing new son.

Alas, the dear child of master and sage

After attaining half the measure of his father’s life chill fate took him.

After consoling his fate by the science of numbers for four years, he ended his life.’

 

This puzzle implies that Diophantus lived …..Could  you tell it to us?

You will publish a post with your solution on this blog and there is an interesting reward for you!

 However, the accuracy of the information cannot be independently confirmed.