In the Land of Oz only one or two-letter words are used. The local language has 69 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?  Answers.
A) 65  B) 66  C) 67  D) 131  E) 138
The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...   The number of 1 letter words (X) that can be made from 69 letters is 69;   The number of 2 letter words (XX) that can be made from 69 letters is 69*69, since each X can take 69 values.   Total: 69+69*69.   Similarly:   The number of 1 letter words (X) that can be made from 68 letters is 68;   The number of 2 letter words (XX) that can be made from 68 letters is 68*68, since each X can take 68 values.   Total: 68+68*68.   The difference is (69+69*69)-(68+68*68)= 
<gadget id="calculator">(69+69*69)-(68+68*68)</gadget>
<output>138</output>
138.   Answer: 138.
<result>E</result>
In the Land of Oz only one or two-letter words are used. The local language has 69 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?