By Orlando E. Villamayor

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**Additional info for Algebra Lineal OEA 5**

**Sample text**

10 . Magic configuration-a. 12. Let the barrel originally conta,in x pints of wine. After one remova,l a,nd replacement, tbe amo unt of wine a,nd its strength are a 1 = x - 3 and s 1 = a 1 f x = (x - 3)/x. On the second removal the amount of w·ine removed will be 3s 1 = 3(x - 3)/x and the amount of wine in the barrel is a2 x- 3 - 3(~; - 3) /~:; its strength is s2 = a2 /x = (x - 3 - 3(x - 3)/:c ) fx . 92 3(x- 3 - 3(x - 3)/x) = , X while t he amount of wine and its strength in the barrel are, respectively, fL 3 = 3(:r; - 3 - 3(x - 3)/x) X Since the strength of wine remaining in the barrel is expression we come to the equation Hence ~: = 3.

Xian. nd. nt docum ents in matheo1atics education io ancient China.. tanfa (Yang Hui's Methods of Computation, 1275) contains the following magic configuration (see [186]). 5. 8. ·cle ·including i·ts center and eve1·y diamete1· has the same sum. Claude Gaspar B achet (1581-1638) (--7 p. ticaJ puzzles a nd tricks ever published. His book P1·oblemes Plaisants et Delectables (1612) contains many mathematical puzzles, arithmetical tricks and recreational tasks. Triangle with integer sides A Heronian t1iangle is a.

Collection of fifty-three amusing problems, riddles and trick questions. th at the monastery of Augsburg, includes Ius tasks. Many puzzles and tasks have survived to the present day. 20. $ his se•l"uant to assel"nble an anny from thiTty shinis ·in such a. trnbe,·· of m en ft·orn each shi1·e as he has collected until that point. st shi1·e alone; to the second in the company of one soldie1·... How many soldie1·s wilt be collected in all'? s first assume tbat the serva nt is oot included in the count at eacb stage.