Solution to puzzle 27

-

 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.

Comments

Post a Comment

Popular posts from this blog

Puzzle 9 : The 4 coins problem

-
 Solution to puzzle 8: Maria is not counting Sundays. So she is not counting 1/7th of days of her age.  That is to say she is only counting 6/7th of her age. 6/7th of her age = 30 Her actual age = 30 X 7/6 = 210/6 = 35 years.  Puzzle 9 : The 4 coins problem  You’re creating a new coin system for your country. You must use only four coin values and you must be able to create the values 1 through 10 using one coin at a minimum and two coins maximum. What 4 coins do you choose, and can you think of a second set of 4 coins that achieves the same goal?
Read more

Puzzle 66 - solution

-
 The question was  What is wrong with this proof ? a=b multiply both the sides by a     --1 a2 = ab  add -b2 to both the side           --2 a2-b2 =ab-b2  factorizing                                --3 (a+b)(a-b) = b(a-b)  divide both the sides by (a-b)    ---4 a+b=b Substituting a with b,              ---5 2b = b Dividing both the sides by b    ---6 2 = 1   The problem is with step 4. When a is equal to b, a-b is zero. You can not divide numbers by zero because division is only defined for non-zero numbers.  
Read more

Puzzle 35 - Open sesame

-
I am writing a post after two months.  Here is a locked question ;) There is a number lock. You have to find the number to unlock it.  And here are the results of various number combinations. 682 - one digit is right and in the right position. 614 - one digit is right but in the wrong position. 206 - two digits are right but both are in the wrong positions. 738 - all digits are wrong. 380 - one digit is right but in the wrong place So what is the correct code to open the lock? Find the solution here
Read more