Grandma's Birthday And Troll Toll

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, 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 that you arrive at Grandma's with exactly 2 cakes?

How many you should carry? Know here!

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Cakes For Grandma's Birthday

What's between you & grandma's birthday celebration? 

No need to overthink on this. Just carry 2 cakes.

At each toll they would take 1 ( half of 2 ) & would give back 1.

So after each toll you would carry 2 cakes & last toll wouldn't be an exception.

A Clever Trader At Checkpoints

Anabelle is a clever trader of rare artifacts. Each day she carries three boxes with each filled with thirty artifacts. The boxes can't hold more than that. She travels far of northern lands to sell these artifacts but on way, she comes across thirty checkpoints where she has to shed one of the artifact for each sack to the authorities for letting her pass.

How many artifacts will be left with her when she reaches her destination crossing all the check points ?  

How she managed to save some? Find here! 

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A Cleaver Trader's Deal At Checkpoints

What was the situation?

Without any work to brain if she travels as it is through all checkpoints then at the end nothing would be left with her. Because at each checkpoint she has to shed 3 artifacts so at 30 checkpoints she has to shed 3 x 30 = 90 artifacts if she gives artifact from each box. And she has only 90 artifacts.

As a clever trader, she starts shedding artifacts from one box at each checkpoint. At first 10 checkpoints, 1 box would be emptied & 30 artifacts paid at checkpoints.

For next 15 checkpoints, she sheds all artifacts from second box thereby paying 30 artifacts.

For final 5 checkpoints, now she has to shed only 5 artifacts from third box with 25 artifacts remaining in the box.

So 25 artifacts will be left with her when she reaches her destination crossing all the check points.