[galactus]

Here's a fun little problem if anyine would like to have a go. It's not too bad.

Maybe you've seen it before, if so, maybe those who haven't will find it fun.

"Little Red Riding Hood is walking to her grandmother's house. She crosses a
bridge and a troll tells her to pay 1/2 of all her apples and 1/2 of one
apple. At each bridge there is a troll asking for the same thing. There are
three bridges. When she gets to her grandmother's house, she has no apples
left. How many apples did she start with"

[Capuchin]

7? Just a first guess.

[Lowtax4eva]

I figured 5 actually

Edit, nope, it's 7 you were right

[galactus]

I realize this problem isn't that difficult. I just thought it was cute.

But, why doesn't someone post their solution instead of just the answer? Go ahead. Different methods is what's interesting.

[asterisk_man]

I cheated with maxima so highlight the text below to see a cheater's answer :)

---start hidden---

at each bridge she will start with a apples and end with 0.5a-0.5 apples so the troll function is:
t(a)=0.5a-0.5=(a-1)/2
so if she starts with a_0 apples she ends with a_3=t(t(t(a_0)))
if you do all the math and set a_3=0 and solve for a_0 you'll find that

a_0=7

in maxima:
t(a):=(a-1)/2
y:t(t(t(a)))
solve(y=0,a)

---end hidden---

[Lowtax4eva]

Lol

What's maxima? I assume a program that solves math functions?

[Lowtax4eva]

I just assumed in order to end with zero he has to arrive at the last bridge with one apple (1/2 of all he has plus 1/2 is one apple)

Going backwards I then saw he has to arrive at the second bridge with 3, giving the troll 2 (1/2 of all he has plus a half is 2).

Same for the first, he has to leave with 3 so he has to arrive with 7, (half of all be has plus a half is 4)

[asterisk_man]

lol

What's maxima? I assume a program that solves math functions?

Maxima is an open source computer algebra system.
Maxima - A GPL CAS based on DOE-MACSYMA