MathDB
43 lines between A and B, 29 lines between B and C

Source: 2011 Swedish Mathematical Competition p4

April 30, 2021
combinatorics

Problem Statement

Towns AA, BB and CC are connected with a telecommunications cable. If you for example want to send a message from AA to BB is assigned to either a direct line between AA and BB, or if necessary, a line via CC. There are 4343 lines between AA and BB, including those who go through CC, and 2929 lines between BB and CC, including those who go via AA. How many lines, are there between AA and CC (including those who go via BB)?