Wise Geometrician: Solution

The male donkey was carrying 7 loads, and the female donkey was groaning under the weight of 5 loads.

See:

Take Y to be the male donkey’s loads, X to be the female donkey’s loads.

       We know that:           

Y+1 = 2(X-1) and Y-1 = X+1

This implies that (adding them up, after multiplying the second by –1)

2 = X-3 => X = 5=>Y = 7

Back to the problem

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Wise Geometrician: Hint

Express the problem by means of a mathematical system.

Back to the problem

Solution

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Wise Geometrician

You are now a wise geometrician and, as such, you might be able to solve the problem that the donkey poses to you.  

  

A male and a female donkey, loaded with bags of wheat, were heading towards the market. The female donkey was groaning because of the heavy load.  Each of the bags weighted the same.

-   What are you complaining about? – said the male – If you gave me one of your bags, I would have twice as many as     you have; if I gave you one of mine, our load would be the same.

-   Things being so, tell me, wise geometrician, how many bags of wheat do each of us carry? – said the female.

                                                          Hint         Solution

                                                            Source of the Problem

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Solution: Curved Figures

Some people might think that the second figure has the longest upper border, because looks disguise. But they are exactly of the same size! They were built using a copy and paste procedure.

Back to the problem

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Hint: Curved Figures

Perhaps use your finger to accompany the borders of the figures. You may wish to copy and paste and then put one over the other.

Solution

Back to the problem

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How Curved Can a Curved Figure Be?

.................................................................................

We ask:

Which figure has the longest upper border, P or Q?

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Hint               Answer

        

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                                                                                                               Source of the Problem

Source of the Problem

The problems we present on this blog came from a Brazilian Mathematician called Malba Tahan. Malba Tahan is actually a pseudonym. According to the source we here mention, his original name was Julio Cesar de Mello e Souza.



These problems were presented at the Science Fair that happened in Melbourne in 2001. They were part of a piece of software built by Marcia R. Pinheiro. This piece of software was displayed at a kiosk where everyone representing VUT was supposed to be.



Coordinating the kiosk was Prof. Neil Diamond, who worked in the same department as Marcia R. Pinheiro back then. 



The problems are based on the book As Maravilhas da Matemática (The Wonders of Mathematics) by Malba Tahan (6th edition, Bloch, 1987, Rio de Janeiro, Brazil).



Marcia R. Pinheiro has translated and adapted them.

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