| 9. If a disc A is attached to a disc B (attached to the main cardioid), then the period of A must be a multiple of the period of B. |
| (a) 12 = 4 ⋅ 3, 20 = 4 ⋅ 5, 28 = 4 ⋅ 7, so these could be discs attached to a 4-cycle discs. |
| (b) 19 is prime, so it cannot be the period of a disc attached to anything. |
| (c) 12 = 4 ⋅ 3, 21 = 7 ⋅ 3, 28 = 7 ⋅ 4 have no common factor, so cannot all be attached to a single disc. |
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