I gave the following problem to both Katie (5) and my nephew Ari (4). The respective conversations follow.
Problem: There are three red balloons and one yellow balloon. Katie, Ari, Ben, and Zoe each get a balloon. Ari and Katie get balloons of the same color while Katie and Zoe get balloons of different colors. Who gets the yellow balloon?
Katie: That’s not right. The problem should say that Zoe and Ben have different colors.
Me: Ok, who has the yellow balloon then?
Katie (after a long pause): I don’t know.
Me: That’s because in your formulation there is not enough information for a unique answer. Lets go back to my version.
Katie agrees and I restate the problem. After a bit more back-and-forth and minor guidance, she solves the problem.
Immediately after I say that Ari and Katie get the same color he interrupts me and says, “So they both get red.”
Me (very excited): Great!
However, when I finish the problem Ari looks a bit confused. I start talking him through it.
Me: You said that Ari and Katie get red, and we know that Katie and Zoe get different colors. So what color does Zoe get?
After going through most of the colors of the rainbow (I couldn’t tell whether he was fooling around or just forgot which one was in the formulation) Ari gets to the correct one.