# Water machine puzzle & representative solutions

## Puzzle

Solve the following problem and remember your thought processes.

Bobbiy wanted to make a water machine. The diagram below shows how s/he took a container, put four holes in the side, a funnel on top, and connected a pipe to the funnel. Bobbiy wants to connect plastic tubes from the pipe to the holes so when water is poured into the funnel it will or won't come out of none, some, or all of the holes. Bobbiy wants to know all of the possible combinations that could be made before deciding.

What are they?

## Representative solutions from actual studies of middle level students

A, D

A, B, C, D

### Fran

A, B, C, D, AB, AC, BC, BC, CD, AD

### Dee

ABCD, BCDA, CDAB, DABC,
AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, DC
ABC, ABD, ACD, BAC, BCD, BDA, CDA, CAB, CBD, DAB, DBC, DCA

### Trav

ABCD, AB, AC, ABD, ABD, BC, BD, CD

### Joe

ABCD, ABC, AB, A, BCD, BC, B, CD, C, D

### Sara

AB, AC, AD, BC, BD, CD

### Daniella

ABCD, ABC, ABD, AB, A
BCD, BC, BD, B
CD, C
D
None

### Barbie

AB, AC, AD, ABC, ABD, ACD, BC, BD, CD, ABCD

### Chou

AB, AC, AD, BC, BD, CD,
ABC, ABD, ACD, BCD, ABCD
A, B, C, D

### Daniella:

A, B, C, D, ABCD,
AB, AC, AD, BC, BD, CD,
ABC, ABD, ACD, BCD, None

## Educator Activity

How would you classify the different solution sets as preoperational, concrete operational, or formal operational? Or any other categorization that would be beneficial for facilitating learning.