The rigged scale

The workings:

“Lazaro, you tricked me. I’ll swear to God that you ate these grapes three at a time.”

“No, I didn’t,” I said. “But why do you think so?”

That wise old blind man answered, “Do you know how I see that you ate them three at a time? Because I was eating them two at a time, and you didn’t say a word.”

 Lazarillo de Tormes is a timeless masterpiece. Fragments such as the one quoted above illustrate attitudes in which we recognise politicians, public figures of all kinds and the main character of the divertimento almost five hundred years later. These behaviours are not criticised by everyone; there are those who applaud them, perhaps hoping for the complicity of others when the time comes to look out for number one. The flipside of the picaresque coin is mistrust. The 2014 European Social Survey puts the percentage of Spaniards who do not trust others at over 60%. The latest eurobarometer reveals equally worrying figures: 91% of Spaniards distrust political parties, 58% distrust public administration and 55% distrust the judicial system. Of course, this distrust of citizens towards public bodies is reciprocal, as if it were the norm that the users and employees of these services try to cheat at every step. Think of your favourite ministry, department or university, and that time when the documentation provided to certify a certain circumstance was incomprehensibly rejected.

The fun:

A trader sells rice using a scale with one arm longer than the other and a single 1 kg weight. In order not to arouse suspicion, she switches the weight from one side to the other after each sale, using the fault in the scale on the first transaction of each day to her advantage. “So,” she says to herself, “if I sell 10 kg of rice in one morning I don’t make any additional profit, but if I sell 11 kg I make something on the last transaction. It’s not much, but it’s not good to be too greedy either, and business is not so bad: every day I sell some rice. There are days when, indeed, this ruse does not bring her any profit or loss. Prove that the ratio between the lengths of the arms of the scales is a rational number.

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Solutions

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.

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