# Does this problem enhance mathematical creativity?

There are an equal number of red, yellow, green, and blue cards. Take one of them and put it in the box. Suppose that red cards was most selected, followed by yellow, green, and blue when we selected cards outside the box randomly. What is the color of the card in the box?

This problem was suggested in the lecture yesterday by other students. I asked solutions for the problem in Mathematics Stack Exchange, and I want to ask something different. The lecture aims to making a set of math problems that enhance mathematical creativity of middle or high school students, and the presenters claimed that this is an example that students can enhance mathematical creativity by the problem.

My question: How to determine whether this problem help students to enhance their mathematical creativity? How to improve this problem?

• Once the question is expressed more accurately, as "what is the most likely color of the card in the box" (footnote 1 of your MSE question), I'd expect that many people would immediately guess the correct answer, without knowing any probability theory. Putting a card in the box leaves fewer cards of that color outside, so it reduces the frequency of that color in your outside-the-box selection. Since blue had the lowest frequency, the card in the box is most likely to be blue. Your rather long solution on MSE seems to show mainly [continued in next comment] – Andreas Blass Oct 31 '17 at 16:57
• [continuation of preceding comment] that it sometimes takes a good deal of work to rigorously justify what reasonable people would have guessed. This can be a valuable lesson, but I doubt it has much to do with mathematical creativity. Perhaps a more valuable lesson would be that sometimes rigorous mathematics disproves what one might at first guess. – Andreas Blass Oct 31 '17 at 16:59
• An implicit consideration RE: "enhance their mathematical creativity" is what exactly is meant by "mathematical creativity" (e.g., in this context). See my lengthy MESE response here for tip-of-the-iceberg considerations in this direction. – Benjamin Dickman Oct 31 '17 at 23:05