Question

A prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded the orchard. The troll demanded payment of one-half of the apples, plus two more. The prince gave him the apples and set off again. A little further on, a second troll guard stopped the prince and demanded payment of one-half of the apples the prince now had, plus two more. The prince paid the troll and set off again. Just before leaving the enchanted orchard, a third troll stopped the prince and demanded one-half of his remaining apples plus two more. The prince paid him and returned home. He had only two golden apples left. How many apples did the prince pick?

How does the problem change if there happened to be 4 trolls Instead Of 3? If the Prince still ends up with two apples, how many did he start with?

Answer 1

How many apples did the prince pick?

the prince ended up with 2 apples:

• the number of apples he had before meeting the third troll = (2 x 2) + 2 = 6 apples
• the number of apples he had before meeting the second troll = (6 x 2) + 2 = 14 apples
• the number of apples he had before meeting the first troll = (14 x 2) + 2 = 30 apples

the prince picked 30 golden apples

How does the problem change if there happened to be 4 trolls Instead of 3? If the Prince still ends up with two apples, how many did he start with?

you must add one more troll into the sequence:

• the number of apples he had before meeting the fourth troll = (2 x 2) + 2 = 6 apples
• the number of apples he had before meeting the third troll = (6 x 2) + 2 = 14 apples
• the number of apples he had before meeting the second troll = (14 x 2) + 2 = 30 apples
• the number of apples he had before meeting the first troll = (30 x 2) + 2 = 62 apples

the prince picked 62 golden apples