trolls taking apples

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galactus

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Hello All. Here is a cute problem you may have seen before. It is not particularly difficult, but just a fun little problem.

"A Princess picked a basketful of golden apples in the enchanted orchard. On her way home, she was stopped by a troll. The troll demanded payment of one-half of the apples plus two more. the princess gave up the apples and continued on home. The princess was then stopped by a second troll who demanded one- half of the apples plus two more, the princess did as she was told and continued on home. Stopped by a third troll who demanded the princess give one- half of the apples plus two more. The princess did as asked and sadly continued on home only having two golden apples left. How many apples did she pick to begin with?"
 
galactus said:
Hello All. Here is a cute problem you may have seen before. It is not particularly difficult, but just a fun little problem.

"A Princess picked a basketful of golden apples in the enchanted orchard. On her way home, she was stopped by a troll. The troll demanded payment of one-half of the apples plus two more. the princess gave up the apples and continued on home. The princess was then stopped by a second troll who demanded one- half of the apples plus two more, the princess did as she was told and continued on home. Stopped by a third troll who demanded the princess give one- half of the apples plus two more. The princess did as asked and sadly continued on home only having two golden apples left. How many apples did she pick to begin with?"
Click to expand...

This is an algebra story-problem - but what the heck - it is a slow day....

Let the no of apples picked originally = A

After first troll # of apples left = A/2 - 2 = (A - 4)/2

After second troll # of apples left = 1/2 * (A - 4)/2 - 2 = (A-12)/4

After third troll # of apples left = 1/2 * (A - 12)/4 - 2 = (A-28)/8

(A-28)/8 = 2 ? A = 44

Also found out that
button is not working - so used Soroban's trick....
 
Yep. You got it SK, but that goes without saying. I just thought it was a funny little story problem.
 
Works like this, going in reverse (n:apples left):
1:2, 2:8, 3:20, 4:44, 5:92, 6:188 ........... n: 3(2^n)-4
 
Sorry, forgot to mention...

before the second troll, the princess and me bumped into each other
and had a bit of nookie in the long grass.
We ate x apples afterwards before she met the third troll.
 
I was wondering why 3 more apples "walked away" all by themselves!! hence x=y-3.
 
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