At a musical recital five students (John, Kate, Larry, Mary and Nick) performed five musical pieces. Two by Bach, two by Mozart and one by Vivaldi. There were three violinists and two pianists. Each student performed only one piece, and played only one instrument. Find the order of the students, their respective instruments and the composer, with the following conditions:
1. The composers were not played consecutively. Vivaldi was played last and Mozart was played first.
2. There was one piano piece that was played between two violin pieces, and two violin pieces between the first and last piano piece.
3. There were no piano pieces by Mozart.
4. Kate played third.
5. John played a piece by Mozart, and was immediately followed by Nick, who played the piano.
Hint: Does ONE work, does TWO work? How many E's are there already?
"Cleverly, there are exactly twelve E's in this sentence."
Can you draw a line through all of the edges in this picture?
Each side is broken into 2 or 3 edges, and there are also 7 edges inside that you have to cross. The line must be continuous, and cross each edge exactly once.
Hint: Try this with a piece of paper.
There is no possible way to complete the line, there will always be one edge left - or you have to cross an edge twice.
This puzzle is the same as the famous 'Seven Bridges of Konigsberg' problem first solved by Euler.
In that problem, the task was to find a closed path that crossed each of the seven bridges of Konigsberg (now Kaliningrad, Russia) exactly once.