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how many cakes to make for grandmas house

JussstMe | 21:29 Thu 23rd Mar 2006 | Quizzes & Puzzles

6 Answers

You are on your way to visit gramma, who lives at the end of the valley, its her birthday and you want to give her the cakes you made.

Between your house and her house, you have to cross 7 bridges, and there is a troll under each bridge.

Each troll insists you pay a troll toll. Before you can cross their bridge you have to give them half of your cakes,,but as they are kind trolls they each give you back a single cake.

How many cakes do you have to leave home with to make sure you arrive at grandmas house with exactly 2 cakes???

Quiz question - Beauty treatment

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juliefer

Two. You give the first troll half your cakes (one) and he gives you a single one back (ie the same one you gave him). So you have the same number you started with. The same applies to the next six trolls.

gen2

You only need to leave with 2 cakes.
First troll takes half a a toll leaving you with 1 kake, but he gives you one back so you now have 2 again.

This is repeated at each bridge until arriving at gramma's (sic) with the same 2 cakes.

gen2

Sorry juliefer, I'm too slow (and careless) with my typing - trying to watch 'The Bill' at the same time.

sire

2 by my calculations

Salty

Being a mathematician....

If you leave with no cakes, the first troll takes half (ie. zero = half of zero), and then gives you one back. The second troll takes half a cake, and gives one back leaving you with one and a half. Third troll takes three quarters of a cake, and gives one back so you have one and three-quarters. You see the pattern...

After 7 trolls you end up with 1/64th of a cake short of two cakes, which Grandma probably wouldn't notice (apart from the fact they are all in bits!).

Of course, if you keep going back and forth over the bridges an infinite number of times before going to Grandma's, you will get closer and closer to two full cakes....She'd be dead by the time you got there, though!

juliefer

The amount that would be lost in dropped crumbs with part cakes could upset your calculations, Salty.

And, as you said, in any case the amount of cake would only approach two whole ones, but would never reach it.

At least me and gen2 let grandma have her cake - whether or not she ate it as well! :)

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