Enigma 1288: How many a’s here?
8 October 2014
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From New Scientist #2446, 8th May 2004 [link]
Consider the two sentences: “The number of a’s in this sentence is one” and “The number of e’s in this sentence is seven”. The first of those sentences is true and the second is false. We consider all the possible sentences of the form of those two sentences with any of the 26 letters of the alphabet in place of a and e and any word for a number between 1 and 20, inclusive, at the end of the sentence. So we are looking at 26 × 20 = 520 sentences in all.
How many of these sentences are true?
Note: I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The latest estimate is that I’ll have a connection by the end of October 2014.