This homework is due on Thursday, April 15, right before class.

- Alex: 5.5/12, 5.5/18, 5.5/20, 5.5/35, 5.5/33, 10) below,
- Amilcar: 5.5/4, 5.5/11, 5.5/18, 5.5/20, 5.5/28, 1) below, 5) below,
- Bobby: 5.5/4, 5.5/11, 5.5/19, 5.5/22, 5.5/29, 3) below, 8) below,
- Caitlin: 5.5/3, 5.5/13, 5.5/19, 5.5/20, 5.5/28, 4) below, 5) below,
- Callie: 5.5/12, 5.5/18, 5.5/20, 5.5/35, 5.5/33, 11) below,
- Carlos: 5.5/12, 5.5/18, 5.5/20, 5.5/30, 5.5/33, 12) below,
- Colin: 5.5/13, 5.5/18, 5.5/28, 5.5/35, 5.5/33, 10) below,
- Diego: 5.5/4, 5.5/13, 5.5/19, 5.5/20, 5.5/29, 1) below, 6) below,
- Frank: 5.5/4, 5.5/13, 5.5/19, 5.5/20, 5.5/29, 2) below, 8) below,
- Jessica: 5.5/3, 5.5/13, 5.5/18, 5.5/20, 5.5/31, 2) below, 9) below,
- Jonathan: 5.5/4, 5.5/13, 5.5/18, 5.5/22, 5.5/31, 1) below, 9) below,
- Jordan: 5.5/12, 5.5/18, 5.5/20, 5.5/35, 5.5/33, 12) below,
- Lacie: 5.5/11, 5.5/19, 5.5/20, 5.5/35, 5.5/33, 9) below,
- Madison: 5.5/4, 5.5/12, 5.5/19, 5.5/21, 5.5/28, 4) below, 6) below,
- Milani: 5.5/3, 5.5/13, 5.5/19, 5.5/20, 5.5/28, 3) below, 5) below,
- Mikhail: 5.5/4, 5.5/13, 5.5/19, 5.5/20, 5.5/28, 3) below, 7) below,
- Mounia: 5.5/3, 5.5/11, 5.5/18, 5.5/22, 5.5/30, 2) below, 7) below,
- Nada: 5.5/3, 5.5/13, 5.5/18, 5.5/22, 5.5/28, 4) below, 8) below,
- Rozie: 5.5/12, 5.5/19, 5.5/28, 5.5/35, 5.5/33, 9) below,
- Salem: 5.5/4, 5.5/13, 5.5/19, 5.5/20, 5.5/28, 3) below, 7) below,
- Sarah: 5.5/4, 5.5/12, 5.5/18, 5.5/21, 5.5/28, 2) below, 6) below,
- Sonja: 5.5/12, 5.5/18, 5.5/28, 5.5/35, 5.5/33, 10) below,
- Stephen: 5.5/11, 5.5/19, 5.5/20, 5.5/30, 5.5/33, 11) below,
- Verena: 5.5/3, 5.5/11, 5.5/18, 5.5/21, 5.5/31, 1) below, 7) below,

**2) ** Which one of the following two knot projections is alternating?
Based on this, can you tell whether any of them might be equivalent to the trefoil knot?

**3) ** Which one of the following two knot projections is alternating?
Based on this, can you tell whether any of them might be equivalent to the figure eight knot?

**4) ** Which one of the following two knot projections is alternating?
Based on this, can you tell whether they might be equivalent?

**5) **Show that the following can be extended into a valid 11-coloring of the knot?

**6) ** Show that the following can be extended into a valid 3-coloring of the knot.
Then give one of two possible reasons why this knot is not equivalent to the figure eight knot.

**7) ** Can the following be extended into a valid 3-coloring of the knot?
If it can, show how. If it cannot, show why not.
Is this knot equivalent to the trefoil? Is it equivalent to the figure-eight knot?
Are there any hard reasons for your conclusion?

**8) ** Can the following be extended into a valid 5-coloring of the knot?
If it can, show how. If it cannot, show why not.

**9) ** Can the following be extended into a valid 5-coloring of the knot.
Does this imply that this knot is not 5-colorable?
Is it 5-colorable?
Then give one of two possible reasons why this knot is not equivalent to the figure eight knot.

**11) ** Is any of the two knots below 3-colorable?
Is any of them 5-colorable?
Based on this, can you draw any conclusion whether the two knots are equivalent or not?
Could you also use the Theorem on alternating knots to back up your claim?

**12) ** Is any of the two knots below 3-colorable?
Is any of them 5-colorable?
Based on this, can you draw any conclusion whether the two knots are equivalent or not?
Could you also use the Theorem on alternating knots to back up your claim?