A bag contains three types of counter: purple squares, purple triangles and red triangles. $70 \%$ of the purple counters are triangles. $60 \%$ of the triangular counters are purple. There are 14 red counters. How many square counters are there?

Step 1 ：Let P be the number of purple counters, T be the number of triangular counters, and S be the number of square counters. We have the following equations:

Step 2 ：\(0.7P = 0.6T\)

Step 3 ：\(0.4T = 14\)

Step 4 ：Solve the second equation for T: \(T = \frac{14}{0.4} = 35\)

Step 5 ：Substitute T into the first equation: \(0.7P = 0.6(35)\)

Step 6 ：Solve for P: \(P = \frac{0.6(35)}{0.7} = 30\)

Step 7 ：Since there are 14 red triangles, there are \(35 - 14 = 21\) purple triangles.

Step 8 ：Since 70% of the purple counters are triangles, there are \(30 - 21 = 9\) purple squares.

Step 9 ：\(\boxed{9}\) square counters in the bag.