Judy had a number of raisins. After eating one, she gave half the remainder to her sister. After eating another raisin, she gave a third of what was left to her brother. Judy now had only six raisins...

Judy had a number of raisins. After eating one, she gave half the remainder to her sister. After eating another raisin, she gave a third of what was left to her brother. Judy now had only six raisins left. How many raisins did she start with?