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This Week's Problem: "28. Toss Toss Toss"

Six young children – K, L, M, N, O, P – gather in a circle and play a game in which they toss a ball to one another. One child starts the game by tossing the ball to one of the other five children, who then tosses it to another child, who tosses it to another child, who is declared the “winner.” A child may handle the ball more than once during the course of any one game, but cannot toss the ball to himself/herself. The following conditions apply:

  • K can only toss it to P.
  • P can only toss it to O.
  • N can only receive a toss from M.
  • L can only toss to P or M, and M can only receive a toss from L.
  • N can only toss to K, and K can only receive a toss from N.





1. Which of the following could be the order of tosses, from the child who starts to the child who wins?

(A) M to L to P to K

(B) M to P to O to N

(C) M to N to K to L

(D) L to N to K to P

(E) L to M to L to P

2. If K starts the game, it could be true that

(A) L receives the second toss

(B) M receives the second toss

(C) M is the winner

(D) N is the winner

(E) P is the winner

3. If O is the winner, each of the following could be true except:

(A) N started the game

(B) M started the game

(C) L started the game

(D) K started the game

(E) P started the game

4. How many different orders of tosses would result in N being declared the winner?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

5. If O starts the game, how many different children can receive the second toss?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

6. Which of the following can’t happen in the same game?

(A) N starts and N wins

(B) M starts and M wins

(C) L starts and L wins

(D) K starts and P wins

(E) K starts and L wins


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