At the recent BrainBashers Festival, the 100 metres heats were closely monitored. Each contestant had to run in two races so that the average place could be determined. Only one runner finished in the same place in both races. Alan was never last. Charlie always beat Darren. Brian had at least one first place. Alan finished third in at least one of the races. Both Darren and Charlie had a second place. What were the two results?
To explain - since Charlie always beat Darren and Darren had a second place, one race must have been Charlie first and Darren second. Brian therefore won the other race with Charlie second. Since only one runner finished in the same place in both races, this must have been Alan in third. QED.
The river Pregel runs through the town of Konigsburg. In the river are two islands, connected to each other and the rest of the city by seven bridges. The students of Konigsburg often challenge each other to try to make a trip crossing all seven bridges exactly once - can you find the path they have to take in order to do this?
Answer: There is no such route. This is a very famous mathematical problem which was first posed by Euler (pronounced 'oiler'). It was a founding problem in graph theory, an area of mathematics which is very important in modern times, and is used in everything from cryptography to route optimisations.
On my local railway track there is a tunnel which is 5 miles long. A train, which was 440 yards long, entered the tunnel at a speed of 50 miles per hour. How long did it take for the whole of the train to pass completely through the tunnel?
Hint: There are 1,760 yards in a mile.
Answer: 6 minutes and 18 seconds.
The train has to effectively travel 5.25 miles at 50 mph. Time = Dist ÷ Speed = 5.25 ÷ 50 = 0.105 hours = 6.3 minutes = 6 minutes 18 seconds. QED.
Using the BrainTracker grid below, how many words can you find? Each word must contain the central R and no letter can be used twice. The letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?