In the Land of Oz only one or two-letter words are used. The local language has 64 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?  Choices:
A) 65 B) 66 C) 67 D) 131 E) 128
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 64 letters is 64;   The number of 2 letter words (XX) that can be made from 64 letters is 64*64, since each X can take 64 values.   Total: 64+64*64.   Similarly:   The number of 1 letter words (X) that can be made from 63 letters is 63;   The number of 2 letter words (XX) that can be made from 63 letters is 63*63, since each X can take 63 values.   Total: 63+63*63.   The difference is (64+64*64)-(63+63*63)= 
<gadget id="calculator">(64+64*64)-(63+63*63)</gadget>
<output>128</output>
128.   Answer: 128.
<result>E</result>
In the Land of Oz only one or two-letter words are used. The local language has 64 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?