Problem 6 · The thirteen seed boxes
The running total doubles at every box: powers of 2.
Integer answer, at most 4 digitsIn front of Marc there are 13 boxes in a row, each containing a large number of seeds. Marc takes one seed from the first box, and from each subsequent box up to the thirteenth he takes as many seeds as he has taken from all the previous boxes together. How many seeds will he have taken in total at the end?
Copa Cangur · SCM
Medium
Closed answer
Reasoned solution
Key idea: if from each box he takes as much as everything he was carrying, the running total doubles.
After box $1$ he has $1$ seed. From box $2$ he takes $1$ (total $2$), from box $3$ he takes $2$ (total $4$), from box $4$ he takes $4$ (total $8$)… After box $k$ the total is $2^{k-1}$.
$$\text{Total after box } 13: \quad 2^{12} = 4096.$$
Answer: 4096