PK 2018 Q12
12. 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
Pink Kangaroo 2018, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 40
Each of the trains leaves one town and arrives at another town so there are a total of 80 start/finish points. Forty are already mentioned, so forty must begin/end at Jena.
Solution © UK Mathematics Trust, from the PK 2018 solutions.