Short Words, with a Twist
In the English alphabet, the following 7 capital letters look the same after being rotated :
How many different 3 letter "words" can be made from these letters such that when the word is rotated , the resulting word is the same?
Details and assumptions
The "words" formed do not have to be valid English words. The word SSS would be a valid word satisfying the conditions.
The answer is 49.
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1 solution
The first letter can be any of the seven letters.
The second letter can also be any of the seven letters.
The third letter must be the same as the first letter. This is because when the 3-letter word "abc" is rotated by 1 8 0 ∘ , we get "cba". Hence, a = c .
By the multiplication principle, there are 7 × 7 = 4 9 different possible 3 letter words.