Ambiguous Answers
There is a sequence that Alice wants to solve:
She has a clue on a strip of paper which says: THE ANSWER IS NOT 25.
What is the answer then?
The answer is 27.
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Relevant wiki: Perfect Squares, Cubes, and Powers
Another relevant wiki is Prime Numbers
Lets lay down try some scenarios for the question
1) The numbers are the squares of the natural numbers in increasing order. ( 1^2, 2^2, 3^2, 4^2) So it seems almost natural for us to say the answer is 5^2 ,which is 25, but it is contradictory to the strip of paper so this method is crossed out.
2) We can see that the numbers can be expressed as the sum of consecutive and positive odd numbers (1,1+3,1+3+5,1+3+5+7) So following the logic of this statement, it means that the next number is 1+3+5+7+9 ,which is 25, but again it is contradictory to the strip of paper so this unfortunate method is no more for this question.
3) This is the answer to the question. We can see that the difference between any two numbers are actually consecutive odd prime numbers.
(4-1=3 [which is an odd prime] 9-4=5 [which is an odd prime] 16-9=7 [which is an odd prime])
So following the logic of this claim, 16+11 [the next odd prime] ,which is 27, should be the answer. Thankfully it is not 25.
Bonus: Between 1, 4 , 9 ,16 ,25 and 27 which one is the odd one out?
P.S. there is no wrong answer for the bonus