Solution to puzzle 27

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 The puzzle was

A teacher wrote down a number on the board asked the students to check the divisors of the number one by one. 

  •      The first student said that the number is divisible by 2.
  •       The second student said that the number is divisible by 3.
  •       And so on.
  •         The 30th student said that the number is divisible by 30.
  •        The last student said that the number is divisible by 31.

Now the teacher said that exactly two students who told about consecutive divisors are wrong. Which are those two numbers? 

Solution :

Let us consider that the numbers is not divisible by are 2 and 3. If so, then the number will not be divisible by all even numbers and all products of 3. So 2 and 3 are not our answer. 

Using similar argument, we can remove numbers from 7 and 8. Because if number is not divisible by 8, it won’t be divisible by 16. 

So we can omit the numbers 2 to 10, 11 and 12 (as it is divisible by 3 and 4, it is divisible by 12), 13 14 15.

But if we take the numbers as 16 and 17, then there won’t be any other factors.

So the 15th and 16th students told wrong answer. And the given number is not divisible 16 and 17.

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