Question

Think of this puzzle. What do you need to find a chosen number from this square? Four of the clues below are true but do nothing to help in finding the number. Four of the clues are necessary for finding it. Here are eight clues to use.
a. The number is greater than $9$.
b. The number is not a multiple of $10$.
c. The number is a multiple of $7$.
d. The number is odd.
e. The number is not a multiple of $11$.
f. The number is less than $200$.
g. Its ones digit is larger than its tens digit.
h. Its ten digit is odd.
What is the number?
Can you sort out the four clues that help and the four clues that do not help in finding it? First follow the clues and strike off the number which comes out from it.
Like- from the first clue we come to know that the number is not from $1$ to $9$ (Strike off numbers from $1$ to $9$). After completing the puzzle, see which clue is important and which is not?

Answer 1

The answer is $35$.
Statement 'a' does not help because by following the other clues you can tell that you need more than on digit.
Statement 'b' does not help because the one digit has to be longer than the tens-digit and the only multiple of $7$ and $10$ is $70$ and $0$ is smaller than the $7$.
Statement 'c' helps because being a multiple of $7$ concels out a lot of numbers that could have been possibilities.
Statement 'd' helps because being an odd number it too ancels out a lot of other possibilities.
Statement 'e' does not help because the only multiple of $7$ and $11$ is $77$ and the ones digit has to bigger than the tens digit.
Statement 'f' does not help.
Statement 'g' helps because by using it there will be few numbers left.
Statement 'h' helps by using it only $35$ remains.
So-$3,4,7$ and $8$ heops and they only are enough to get the number.