Vrijeme: 11:06

Fufi | Phuphi #1

Luka je na ploču zapisao troznamenkasti broj (bez nula). Kada ga nije bilo, njegov pas Fufi je zamjenio svaku znamenku i tog broja sa \varphi (i). Kada se Luka vratio bio je ljut što mu je netko dirao ploču, ali ubrzo je shvatio da broj koji je napisan na ploči je djelitelj njegovog originalnog broja. Koliko troznamenkastih brojeva je Luka mogao na početku napisat?
Luka wrote a three-digit number (without zeros) on the board. While he was away, his dog Fufi replaced each digit i of that number with \varphi (i) . When Luka returned, he was angry that someone had touched the board, but he soon realized that the number written on the board was a divisor of his original number. How many three-digit numbers could Luka have originally written?