In the game of UNDER, two dice are thrown. If the sum of the dots is under seven, the player receives 8 points. If the sum of the dots is seven or greater, the player loses 6 points. How many points can a player expect to win or lose if 100 games are played? Write the answer to the nearest point and indicate whether it is a gain or a loss.
Alternate Problem 15
Twenty cards are chosen from a standard deck of playing cards–ten black cards, ace to ten, and ten red cards, ace to ten. The cards are arranged in a certain order so that, after completing the steps listed below, the cards turn up in order–black, ace to ten, and then red, ace to ten.
STEP 1: Hold the pack face down. Make two piles of cards by alternately placing one card up and one card down. Start with one card up.
STEP 2: Pick up the cards that are face down. Repeat STEP 1, placing the face-up cards on the first face-up pile.
STEP 3: Repeat the process described in STEPS 1 and 2 until all the cards are face up.
What is the original order of the twenty cards?
Extension Problem 15
Suppose 3 and 8 are the only individual scores that can be made in a certain game. How many different scores are impossible for a person to attain.