Ginoni the goat is at the bottom of a series of 7 boulders, each higher than the last. She wants
to reach the top, where there is a huge patch of
grass that she’d like to graze. Being an athletic
goat, she sometimes bounds up two boulders at
a time; otherwise, she just jumps up one.

Ginoni can use both one-boulder and two-
boulder leaps within an ascent.

Starting at the bottom, in how many ways could
she reach the grass at the top?
Investigate what happens for different numbers
of boulders and explain the pattern of how many
different ways she can ascend.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."