25
It might be possible to do a little better, but I think I can get
Explanation:
12
A complementary result of tehtmi's answer: Using the same strategy,
is the maximum number of coins you can get, and +1 is impossible. Proof:
11
You can solve the problem via integer linear programming as follows. Let $n$ be the number of coins, so we need at most $n$ bags. For $b \in \{1,\dots,n\}$, let nonnegative integer decision variable $x_b$ be the number of coins in bag $b$, with $x_b$ nonincreasing. Let $z$ represent $\max_b \{b\cdot x_b\}$, which is the number of coins the king will take. ...
10
Can't you just do
?
9
Their best strategy is
Their chances with this strategy are
Optimality
7
The poor robot might get slightly less dizzy with
4
A slightly different approach as the other answers
3
Here is my edited improved answer, not sure optimal, there is a methodology but not sure about its optimality anyway:
For this,
I will put the coins in the bags as below:
As a result,
There are 4 possibilities for your knight to choose,
or
or
or
3
I found a solution using
This works as follows:
The reason why the enemy cannot intercept 10 different messages:
Furthermore, this number of days is optimal because of the following argument:
3
Edit: I'm sure @tehtmi's answer is correct. Kind of irrelevant to my answer, but here is a code for you to experiment with different bag combinations. Simply fill in the bags list and run the program:
For bags I used:
And @tehtmi used:
bags = [] # Put in this list all the numbers you want, with each number representing a bag of that amount of coins
keeps =...
3
Alternative solution:
3
The following program should work:
3
I randomly encountered this problem and I think I have a simpler solution (for the special kudos version) than Gareth's:
2
I now wonder how many solutions there are.
Just in case the purpose is to take as long as possible: "the tourist".
1
It gets a bit messy, but in the end it comes down to algebra.
1
One sequence is:
First, it seems clear that we need at least:
This would give something along the lines of:
We obviously need something else, though, because:
However, we just need a bit of additional logic:
Notice, however, there is no one answer:
Only top voted, non community-wiki answers of a minimum length are eligible
