Gavilán o paloma (Sparrowhak or dove)

Algebra Level pending

In Spain, we have this nice problem, in verse. My father used to recite it to me.

Un gavilán vio una bandada de palomas y les dijo: “Bienhalladas sean las cien palomas” Contestó una paloma: “No señor, que no somos cien.Pero con éstas, otras tantas como éstas, la mitad de éstas, la cuarta parte de éstas, y usted, señor gavilán, ¡ciento cabal!*

It translates as:

A sparrohawk saw a flock of doves, and it said to them: “Well met be the hundred doves” A dove answered: “No, sir, we are not a hundred. But with these, as many as these, a half of these, a quarter of these, and you, Sir Sparrohawk, exactly a hundred!

How many doves were in the flock?

Very sorry for my awful English!

35 42 36 34

Enrique Blanco Rodríguez by Enrique Blanco Rodríguez , 58, Spain

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1 solution

Ratul Pan
Nov 24, 2015

let the number of doves be X.
Therefore
X+X+X/2+X/4+1=100
or, 11X/4=99
X=36

1 Helpful 0 Interesting 0 Brilliant 0 Confused

There is still another method, although myself, I prefer equations. But is the method used by peasants, here in Spain, so many years ago.

A hundred doves minus the sparrowhak gives 99. So, the number of doves should be divisible by 9.

It is posible, by what the problem says, to have a quarter of the dove's number. So if must be divisible by 4.

9*4=36, which is the answer.

Enrique Blanco Rodríguez - 5 years, 6 months ago

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