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Problem of the Day #121: qwertyasdfzxcvb July 18, 2011

Posted by Seungln in : potd , trackback

Sreenath likes mashing. (This link might clarify it a little bit.) Sreenath will start from the top row and randomly choose a key to start with and a key to end with. The key to end with can be the same as the key to start with, but cannot be to the left of the starting key, because Sreenath will only mash to the right. He will then repeat the procedure with the home row and then the bottom row. (The top row is the row from ‘$q$’ to ‘]’, the home row is from ‘$a$’ to ‘;’, and the bottom row is from ‘$z$’ to ‘.’.) If Sreenath is to spam Albert with every possible mash that has more than $5$ characters, with how many distinct mashes can Sreenath spam Albert? (e.g. The mash on the title, ‘qwertyasdfzxcvb’, is one that Sreenath will send to Albert. The mash ‘qwaz’ is not, because it is too short. The mash ‘asdfghjkl;’, while long enough, does not take inputs from all three rows, and will not be sent. The mash ‘qwertyzxcvbasdf’, while long enough and containing keys in all three rows, is not done in the right order, and will also not be sent.)

Comments»

1. Eugene - July 18, 2011

problem is slightly ambiguous – in last line it says ‘asdf’ is not counted due to length, but it should also say that it is not counted due to not using the top and bottom rows.

2. Sreenath - July 18, 2011

rtyusdfbnm

3. Seungln - July 18, 2011

I’ve added a few other invalid mashes to clarify it up a bit – thanks for the input.