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There are six dots in a Braille cell. Each dot can be either raised or left blank. A black dot is raised on the paper so you can feel it (circles represent dots that have not been used). A quick calculation should tell you that there are $2^6$ possible arrangements of the six dots. However, some would be difficult to tell apart if you were blind and so no two letters use the same arrangements placed in slightly different positions, for example the letter "d" is represented in the following way: so no letter uses .
Here is the Braille alphabet:
Unfortunately something has gone wrong with the machine I use to produce Braille messages and one of the pins that makes a raised dot is not working. I typed a short message in Braille on my faulty machine. Can you work out what it really says:
The technician came to repair the machine and after she left it was worse than ever (a common story). Now my Braille machine randomly selects one pin that does not work. Can you decipher the following message written on the machine:
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?