An event was held in the month of June but James forgot on which date. To refresh his memory, he asked five of his colleagues about what was the precise date. The responses were as follows:

Abe: The date was an odd number.
Belinda: It was greater than 13.
Charlene: It was not a perfect square.
Daphne: It was a perfect cube.
Ethan: It was less than 17.

The next day James was able to get a copy of the yearly schedule, whereby he noticed that exactly one of the five statements was true.

What was the date of the event?

If exactly one of the five statements is true, then either Belinda or Ethan must be telling the truth, as they can't both be false. 
Assume Belinda is telling the truth and the number is >13 (14 thru 30).  All other statements are false, so it's an even number, 13<x<=30, its a perfect square (only 16 works), but since Ethan's statement is false, it must be greater than 17 = no solution.
Try Ethan is telling the truth.  All numbers 1 to 16 work, it must be even, must be a perfect square (4, 16 work), not a perfect cube (4,16 still work), and must be less than 13 => 4.

The answer is 4.

Posted by Kenny M on 2014-07-28 19:45:16