I tried to take this question as seriously as possible. Nevertheless, we must break the cycle consisting in having a reasoning, and then consider that everyone will have the same and do the opposite. For this, I asked people to rank the numbers from 1 to 30 from the most particular to the least particular. I left the possibility of not making the complete list, but only the beginning and the end. I then became interested in the missing numbers, which were neither "special" nor "arbitrary", and I combined these results with some personal constraints:

• Choose an even number because odd numbers look more arbitrary
• Choose a number greater than 10. This comes from the fact that if the first numbers are more special and a priori little chosen, it is risky to make this choice because of similar reasoning. To illustrate this, I can cite the case of the lotto, and the reasoning of betting on the numbers "1, 2, 3, 4, 5, 6", because "no one plays these numbers because they do not seem random at all". Yet, I have already heard two people hold this reasoning, more than on any other combination. Thus, to bet on obvious things "because obviously nobody else will do it" is generally a bad bet, because of the fact that we can treat these things as a special case (here, numbers 1 to 3 for example).
• Choose a number less than 29, for the same reasons

This left me with few choices: 18, 22, 26. I ended up choosing 18 (for both questions). Afterwards only I realized that this was the current year, and that it may have affected this value in a specific way (I think I finished 10th or 11th out of the 25 people having had all the points for the other problems). The complete results are available on the following graphics:

First question, results ordered by value:




First question, results ordered by frequency:




Second question, results ordered par value:




Second question, results ordered by frequency:



A few remarks:

• While overall even and odd numbers are similarly chosen (92 vs. 95 and 93 vs. 94), 3 of the 4 least chosen numbers in the first question, and 6 of the 7 less chosen numbers in the second are odd.
• For each of the questions, the number that comes largely in the lead is the 2nd greatest prime number (17 and 23). One can extrapolate by saying that these answers are those of people who answered "randomly", without thinking about the question.
• From the two remarks above, one can conclude that the people who thought about the question chose rather even numbers, just like me.
• The multiples of 5 are very seldom chosen. The winner also asked all his customers during a week to choose a number between 1 and 30 (dozens of people), and noticed that this was indeed the case.
• This illustrates in any case well the biases that we have when we have to make random choices.