MaMaMu: Full Spectrum of Problems

Too often mathematics is presented in an unending staccato sequence:

problem -> solution
problem -> solution
problem -> solution
problem -> solution

One correct solution for every problem.

This is bogus!

Mathematics education is kept vibrant by adding authentic diversity. Some problems ...

• are impossible.
• have a unique solution.
• have multiple solutions. The student needs to find ALL of them.
• have an infinite number of solutions.
• are unsolved.
  

One of these mini-sudokus is impossible; one has a unique
solution; one has more than one solution. Which is which?

The full spectrum of problems belong in every elementary school curriculum. That includes unsolved problems in mathematics. By junior high, students should expect that some problems that they struggle to solve will actually be impossible. That's real life!

Do numbers thrown into these rivers always end up at "1"?

This question is unsolved for one of the rivers.
For the other river, the question is regularly solved by grade 4 students.