Library / UKMT Pink Kangaroo /207 of 220

UKMT Pink Kangaroo, 2018

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In a certain region are five towns, Freiburg, Göttingen, Hamburg, Ingolstadt and Jena. On a certain day 40 trains each made a journey, leaving one of these towns and arriving at one of the other towns. Ten trains travelled either from or to Freiburg. Ten trains travelled either from or to Göttingen. Ten trains travelled either from or to Hamburg. Ten trains travelled either from or to Ingolstadt. How many trains travelled from or to Jena?

(A) $0$ (B) $10$ (C) $20$ (D) $30$ (E) $40$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

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.