### Game 1

**Step 1**

Per the given scenario, write out the five elements - F, G, H, J, and K - to be placed, and five positions to be occupied.

**Step 2**

Per the first and third rules, notate that H and F must be immediately next to one another (in either order), and that G must come before this duo.

**Step 3**

Per the second rule, notate that K must come before H and J. We can connect this to the H we already have written down.

### Game 2

**Step 1**

Per the given scenario, we can lay out six positions to be filled. We can also list out the six subjects - N, O, P, S, T, and W-as the elements to be assigned, and use subscript to represent the teacher connected to that subject: Nj, Oj, Pk, Sk, Tk, WL.

**Step 2**

Per the first rule, we can notate that we cannot have two consecutive K’s.

**Step 3**

Per the second rule, we can notate that Sk must be before Oj.

**Step 4**

Per the third rule, we can notate that Tk must be before WL.

### Game 3 (Option 1)

**Step 1**

Per the given scenario, we can write out the eight items to be placed: desserts F and G (Fd, Gd), main courses N, O, and P (Nm, Om, Pm), and side dishes T, V, and W (Ts, Vs, Ws), notate the three dishes that are hot (with an h before F, N, and T), and we can lay out the five positions to be selected and the three positions for those who won’t be selected.

**Step 2**

Per the first rule, notate that we must have at least one of each subset. A small inference that can be made is that since we only have two desserts total (F and G), at least one of those two must be selected. We can place an F/G on the board, and notate conditionally that if either of them are out, the other must be in.

**Step 3**

Per the second rule, notate that at least one hot dish must be selected.

**Step 4**

Per the third rule, notate that P and W must always be together.

**Step 5**

Per the fourth rule, we can notate conditionally that if G is selected, O must be as well, and the contrapositive. We can add this notation to the conditional information we’ve already notated about G.

**Step 6**

Per the fifth rule, we can notate conditionally that if N is selected, V cannot be, and the contrapositive. We can make and notate a small inference that this means at least one of the two -- either N or V -- must be out.

### Game 3 (Option 2)

**Step 1**

Per the given scenario, we can write out the eight items to be placed: desserts F and G (Fd, Gd), main courses N, O, and P (Nm, Om, Pm), and side dishes T, V, and W (Ts, Vs, Ws), notate the three dishes that are hot (with an h before F, N, and T), and we can lay out the five positions to be selected and the three positions for those who won’t be selected.

**Step 2**

Per the third rule, we can create two frames, one where P and W are both selected, and another where neither is selected.

**Step 3**

In the second frame, when neither are selected, we only have one remaining out slot. Looking down at the fifth rule, we know that that final spot must be occupied by either N or V. Thus, in the second frame, all other elements must be selected, and we can draw them in. Testing the selections against the rules, we don’t violate any of the rules, and so we know that the frame is viable.

**Step 4**

Returning the first frame, per the first rule, notate that we must have at least one of each subset. A small inference that can be made is that since we only have two desserts total (F and G), at least one of those two must be selected. We can place an F/G on the board, and notate conditionally that if either of them are out, the other must be in.

**Step 5**

Per the second rule, notate that at least one hot dish must be selected.

**Step 6**

Per the fourth rule, we can notate conditionally that if G is selected, O must be as well, and the contrapositive. We can add this notation to the conditional information we’ve already notated about G.

**Step 7**

Per the fifth rule, we can notate conditionally that if N is selected, V cannot be, and the contrapositive. We can make and notate a small inference that this means at least one of the two -- either N or V -- must be out.

### Game 4

**Step 1**

Per the given scenario, write out the elements to be placed - G, R, S, T, and W - and indicate that G takes up two :30 slots while the rest of the elements take up just one. Also, lay out six slots for the six positions that begin at 1:00.

**Step 2**

Per the first rule, split the board into three frames, representing the three times where the G (or G’s, per how we’ve notated it) can be placed: at 1:00, 2:00, and 3:00.

**Step 3**

Per the second rule, notate on each frame that T must go on the half hour rather than the hour.

**Step 4**

Per the third rule, notate that R must be before S.

**Step 5**

Per the fourth rule, notate conditionally that if W is before T, it must be immediately before T, and the contrapositive (if W is not immediately before T, W must be after T.)