Itsensä kuvaava lauseke

Jostain tuli mieleeni sellainen probleema, että onko mahdollista löytää sellainen aritmeettinen lauseke, että kun sen laskee ja tuloksen numerot ryhmittää kolmen numeron ryhmiin (niin kuin yleensä on tapana isoja lukuja kirjoitettaessa) ja kunkin kolmikon tulkitsee ASCII-koodina, saadaan sama lauseke.

ASCII-koodi antaa 128:lle merkille numerot. Nästä 94 on näkyviä merkkejä, kuten englannin kielen akkoset isoina ja pieninä kirjaimina, numerot sekä tavallisimmat välimerkit ja joitakin muita merkkejä. ASCII-koodia ei ole suunniteltu aritmeettisille lausekkeille vaan tavallisille viestelle kuten tilauksille tai onnitteluille. Yhteen- ja vähennyslaskujen merkit + ja - ovat mukana koodissa, mutta tavallisimmat kertomerkit · ja × puuttuvat. Sen sijaan mukana on *, joten käytetään sitä kertomerkkinä. Jakolaskua ei voi kirjoittaa tavalliseen tapaan viivan ylä- ja alapuolelle, eikä ÷ ole koodissa mukana. Sen sijaan / on, joten käytetään sitä. Potenssiin korotusta ei voi kirjoittaa tavalliseen tapaan nostamalla eksponentti ylös, joten siihenkin pitää olla oma merkki. Tavallisin potenssimerkki ↑ oli mukana vanhassa ASCII-koodissa, mutta uudemmassa koodissa sen numero on annettu merkille ^, ikään kuin nuolen kärki ilman vartta. Käytämme siis sitä potenssiin korotuksen merkkinä. Siten lauseke, joka tavallisesti kirjoitettaisiin 5 · 10¹² voidaan kirjoittaa ASCII-merkein 5*10^12. Ei ihan niin nättiä, mutta ymmrrettävissä.

Koska ASCII-koodiin tarvitaan kolme numeroa joka merkkiä varten, on lausekkeen (tai minkä tahansa tekstin) ASCII-koodi paljon pitempi kuin koodattava lauseke (tai teksti). Yhteenlaskun tulos on aina lyhyempi kuin lauseke ja niin on kertolaskunkin. Siksi lausekkeessa, jonka on tarkoitus esittää omaa ASCII-koodiaan, tarvitaan potenssiin korotusta. Esimerkiksi edellä mainittu 5*10^12 esittää kolmetoistanumeroisen luvun kuudella merkillä.

Lausekkeen kirjoittamiseen tarvittavat merkit ja niiden ASCII koodit:

Onnistuin löytämään lausekkeen, jonka pituus on 21867 merkkiä. Kun sen laskee, saadaan luku, jossa 65600 numeroa, jotka voi ryhmittää 21867 kolmen numeron ryhmään (ensimmäiseen ryhmään tulee vain kaksi numeroa, mutta luvun alkuun voi ajatella ylimääräisen nollan). Kas tässä:

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