- The questions starts off with "You're driving a bus". Thus, the eye colour of the driver is whatever yours is.
The idea behind this question is to emphasise the point that to produce an answer you first have to understand what information you need from the question.
- If you take 307 bananas from 429 bananas, how many bananas do you have? You have 307.
- All months have 29 days.
- The probability that exactly five are in the right envelopes is zero. If five are in the right envelopes the sixth must be two.
Here, again, we are dealing with the idea of taking the important information from the question. The most important word in the question is "exactly". Thus, any solution we generate should be weighed up against the requirement.
- Each dog takes five days to dig a hole. So ten dogs will take five days to dig ten holes.
- The full stop at the end of the sentence is the smallest circle.
- Tuesday, Thursday, today and tomorrow.
- Noah built the Ark not Moses.
- All the numbers are divisible by two. The question does not ask for integer answers.
- And the final puzzle. Did you spot it? The first instruction you are given is to write your name in the square. Next to this instruction is a rectangle. The square is at the bottom :).
Questions 2 and 3 deal with the idea of clarity of communication. When answering a question in mathematics you have to clearly define your terms and your assumptions.
By now the students should realise that the questions are trick question, so questions 5 and 6 teaches them not to be too hasty with their answer and to think carefully even when the answer appears obvious.
This question asks them to find a solution to the seemingly impossible. The idea being that mathematicians need tenacity when working with a problem. Many times you it will seem like the question is intractable but eventually you will find the right path.
Questions 8 and 9, again, show the importance of reading questions carefully and fully understanding what is being asked. Trust me, as a mathematician, the hard part is not generating a solution, but rather, understanding what the question is asking.