Solution:

Of course, it is impossible. Into the second room should have gone the 2nd guest, because the 13th guest was waiting in room number 1

Solution:

Michelangelo juggles the diamonds across while crossing the bridge.

Solution:

She has misplaced 119 pens in total.

Solution:

There can be more than one possible solutions. We are sharing one with you:
Anabelle lost to Betty, but won every other game for a total of 3 points.
Betty beat Annabelle, but tied in all other games for a total of 2.5 points.
Christie beat Dora and tied with Betty and Evelyn for 2 points.
Dora beat Evelyn and tied only with Betty for 1.5 points.
Evelyn tied with Betty and Christie for 1 point.

Solution:

You are the ship captain. Read the first sentence again. Therefore, the color is same as your eyes color.

Solution:

In the corners of the square, tighten two ropes. Tighten another rope between them by putting rings on each rope. That rope should be tightened on the sheep's neck on the other end.

Solution:

A - Gold
D - Silver
C - Bronze

Solution:

The two numbers are 4 and 13 whose product is 52 and sum is 17.

Solution:

Let the distance between Peter's (hereafter referred as P) and Rhea's (hereafter referred as R) be D.
When P and R meet for the first time, P has traveled 500 miles.
In that case, R has traveled (D - 500) miles.
=> Speed of P / Speed of R = 500 / (D - 500) ...... (1)

When P and R meet for the second time, P has traveled (D - 500) + 300 miles
Now, R has traveled (500 + D - 300)
=> Speed of P / Speed of R = 5 / (D - 5) ..... (2)

Equating (1) and (2)
500 / (D - 500) = (D - 2) / (D + 2)
D = 1200 Miles.

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.