The puzzle is as follows:
In a certain kindergarten there are 23 children. Some of them wear a green t-shirt, others a yellow t-shirt and others blue t-shirt. A tv reporter who was on the site doing a documentary made them the following three questions:
Are you wearing a green t-shirt? 17 of them answered yes.
Are you wearing a yellow t-shirt? 12 of them answered yes.
Are you wearing a blue t-shirt? 8 of them answered yes.
It is known for a fact that in such peculiar kindergarten, those who wear a green t-shirt always tell true statements, while children wearing a yellow shirt alternate the truth value of their answers, and those who wear blue t-shirts always tell false statements.
With all of this information, how many of those children were wearing a yellow t-shirt when interviewed by the reporter?
The alternatives given in my book are as follows:
I'm confused exactly on how to approach this question methodically without having contradictions.
I'm assuming that from the given information, those who are wearing a green t-shirt will say true, but there are others who will also say this, so it is not possible to know from this clue alone who is wearing green.
The other clue mentions that those who are wearing yellow colors alternate their truth value. From this I'm assuming that we can be sure that at least 6 are wearing yellow color.
But there is more.
The other half could only be wearing Blue because if they were wearing green it meant that they are telling true and that must be their color.
Those who are wearing blue cannot be blue because that could cause a contradiction, so this means they are wearing yellow.
Therefore, this means:
But is this the right way to approach this puzzle? Or am I wrong in my deduction?
I also noticed that with the given clues, it is not possible to know how many are blue. Am I right with this?
Can someone guide me in a better way to think this problem?
For reference, this riddle comes from my Reason and logic from 2000s which seems to have puzzles from a reprinted version of Martin Gardner's 1970s, Puzzle carnival.
So all and all, can someone help me? Is there a way to do this without just getting confused?.