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Giuseppe Bilotta
Lives in Catania
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A tempo perso (l'ultimo pensiero ‘serio’ sulla questione l'ho avuto quasi due anni fa) avevo cominciato a lavorare al problema della rappresentazione minima di numeri razionali tramite espressioni mononumeriche. La cosa è soprattutto un gioco, ma può essere formulata in termini di probemi di teoria dei grafi che potrebbero essere di maggiore interesse. Per stuzzicare la vostra curiosità, ecco intanto l'introduzione degli appunti che ho cominciato a prendere sulla questione:

A classic lateral thinking problem asks how to obtain the value 100 using only four 9s. The solution[1] plays on the possibility to use the 9 as a digit rather than as a number, which is instead the implicit assumption done by many of those facing the problem. However, if we keep “thinking inside the box”, we can turn the question to a different one, asking for example: what is the mininum number of times in which the number 9 must appear in an expression (that does not involve any other number) to obtain 100? Since we can write 100 = 102 = (9 + 9/9)(9+9)/9, we know that the answer to the question is not more than 6. But can we do it with even less 9s?
More in general, is it possible to determine the minimum number of times in which a given number b (alone) can appear in an expression to obtain a given value a?

[1]: 100 = 99 + 9/9

(e ci piacerebbe che G+ supportasse almeno Markdown)
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maurizio codogno's profile photoGiuseppe Bilotta's profile photoMarco Broglia's profile photo
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Sì, ma come dicevo, quello che a me interessa non è il problema dei "quattro quattro”  (né il problema dei quattro nove, né altro), in cui il il 4 è considerato come cifra. Mi interessa invece ragionare esclusivamente in termini di numero.

In particolare, il problema che mi piacerebbe affrontare è questo: data una base b, qual è il minimo numero di volte in cui tale base deve comparire in una espressione per ottenere un dato numero t?
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/me takes again the script for the multiple tango_ lart
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