Library / /57 of 61

, 2017

Number theory Difficulty 5.0 AIME, harder Prove it United Kingdom

The 9-digit positive integer $N$ with digit pattern $ABCABCBBB$ is divisible by every integer from 1 to 17 inclusive. The digits $A$ , $B$ and $C$ are distinct. What are the values of $A$ , $B$ and $C$ ?

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.