Hello, azuresonata!

This is a tricky Venn diagram problem . . .

A group of students was asked to among the 3 bands: M, S, and H.

21 prefer M

23 prefer S

10 prefer M or H but not S

14 prefer M or S but not H

12 prefers S but not M or H but not M

3 prefers H but not M or S

8 prefers S but not M or H

17 prefers at least 2 of the bands

27 prefers 1 at most.

My teacher told me that there is another way to construct this diagram

which is way faster than using the cardinality of the given sets.

Does anyone know how? I think algebra is the way to go. Code:

* - - - - - - - - - - - *
| M |
| |
| s * - - - - - - - + - - - *
| | | |
| | | |
* - - - + - - - + - - - * | |
| | | | | |
| | t | u | v | w |
| * - - - + - - - | - - - * |
| | | |
| | x | S |
| y * - - - + - - - - - - - *
| |
| H |
* - - - - - - - - - - - *

We have the three "circles" for

Label the seven regions with

Then translate the given facts to equations.

And solve the system.

(We already have two of the values.)

.