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.
These words have had their vowels removed, can you replace them to find some animals:
Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.
Hint: There are three zeros in the number.
Your objective is to place some diagonal 'mirrors' into the grid.
If a ray of light is shone in to the grid from each of the letters, and allowed to bounce off the internal diagonal mirrors, each will exit the grid at the twin of the letter that it entered the grid. For example, a ray entering at either letter D will bounce off some mirrors and exit the grid at the other letter D.
Each row and each column will contain exactly two of the diagonal mirrors.
Using the BrainTracker grid below, how many words can you find? Each word must contain the central H 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?