Two math puzzles to puzzle you

I have always been fascinated by puzzles based on logic rather than pure mathematics. How these puzzles are different from the usual mathematical ones is that at some point in time of solving the puzzle, you have to use your logical part of the brain and eliminate some answers and not just keep doing some calculations to reach the answer. Below are two such puzzles which are extremely interesting to solve (in my opinion). The answers are written in white just after the puzzle. So , to see the answer, highlight the empty area after the puzzle. Enjoy!
Puzzle 1:
A census-taker(CT) (one who counts the population) goes to a house and knocks on the door. A woman(W) opens the door. Given below is the conversation they have:
CT: Ma’am, how many children do you have ?
W: Three
CT: Can you please tell me their ages ?
W: I won’t tell you their ages, but i can give you clues.
CT: wow, a puzzle! Ok, give me the clues.
W: Clue No 1: The product of my kid’s ages is 36.
W: Clue No 2: The sum of their ages is equal to my door number.
CT looks at the door number, thinks for a while and says “i need more clues”.
W: Okay, one more clue. My eldest plays baseball.
CT: Thank you Ma’am. I know their ages now.
Now, all you have to do is to find their ages with the above information.
The woman has three children. The product of their ages is 36.
First, write down the possible combinations. They are 36/1/1, 18/2/1, 9/2/2, 9/4/1, 6/6/1, 6/3/2 and 4/3/3. Now, try to do what CT would have done i.e. take the totals of the ages which respectively are 38, 21, 13, 14, 13, 11 and 10.
The CT knew the door number (he can see it). If one of the totals matched the door number, he would have solved the puzzle. But, he asked for more clues. That means that the door number appeared as the total of more than one combination, which in our case is 9/2/2 and 6/6/1 whose total is 13.
The next clue was “My eldest plays baseball”. This clue may seem weird, but it is actually a very intelligent clue. When the woman refers to “my eldest”, it means that her eldest kid is unique which is not the case with the twins of 6/6/1. So, the answer is 9/2/2.
Puzzle 2:
There are 37 students in a classroom. What is the probability that at least 4 of them would have their birthday in the same month? Though this looks like a mathematical question, it is actually to be solved logically.

Assume the worst case of the students’ birthdays being split right across all the months. If there were 36 students in the class, then 3 of them would have their birthdays in each month(36/12 months = 3 in each month). If a 37th student appears, this his/her birthday could be in any of the 12 months. What that means is that, for sure he would be at least the 4th person to have a birthday in any month. So, the probability is 1 (one) i.e. surely in a class of 37 students, at least 4 would have their birthday in the same month.

Hope you enjoyed the puzzles. If you liked them , you can check out more puzzles from the Logic Puzzle quiz which i conducted some time back.

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