A letter Lock consists of three rings each marked with 10 different letters. Number of ways it is possible to make an un successful at tempt to open the lock is 

Two rings may have same letter at a time but same ring cannot have two letters at a time. There fore we must proceed ring wise.

Each of the three rings can have any one of the 10different letter in 10 ways

Total no. of attempts $=10\times 10\times 10=1000$

But out of these 1000 attempts only one attempt is successful

$\therefore$ Required number of un successful attempts are

$=1000-1=999$