Challenge+Two


 * [[image:pool_table.jpg width="142" height="110"]]Challenge Two**

Here is your next tricky challenge - Pool Balls! **Question A** Amy is playing with the pool balls numbered 1 to 15 on a pool table.After every three balls sunk by Amy, she recorded the subtotal of all the balls remainingon the table. She continued until no balls were left on the table. Show ho she could have done this if all the subtotals (except 120 and 0) were prime.

Think about which problem solving strategy will work best. Check out the problem solving clues or strategy part of this wiki. After removing balls 14 and 15, Amy sinks one ball at a time until there are none left, so that the subtotal of the remaining balls each time alternates between prime and square numbers. Show how she could have done this.
 * Question B **


 * Question C**

Starting with all 15 balls, Amy tries to sink one ball at a time until there are none left, so that the subtotal (except 120 and 0) of remaining balls each time alternates between prime and square numbers. Sho that this is impossible.