L yla counted her collection of stuffed animals. She always had one leftover when she counted by two's, three's, four's, five's or six's. But when she counted by seven's, she came out even. How many animals did she have?

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."

The bake stars picked 907 apples last weekend at a local orchard they made caramel apples and sold them in the bakery in trays of 6

Show your workcan a right triangle have this sides? *how to prove it without using the pythagorean theorema*