New answers tagged optimization
0
Another one of those puzzles you can brute force, and therefore would have a coding answer.
The answer is:
Try online
Brute force code:
function permut(string) {
if (string.length < 2) return string; // This is our break condition
var permutations = []; // This array will hold our permutations
for (var i = 0; i < string.length; i++) {
...
0
If we set x=9 then we have x*(x-4)*(x-8)=45
(x-1)(x-5)(x-7)=64
(x-2)(x-3)(x-6)=126
so I obtain 951*842*763=610966146
My opinion is that if we obtain minimum results from the multiplications of monomials, then we will obtain the maximum product of the three 3-digit numbers.
3
The answer is
as @avi already mentioned. But here is my justification:
The conclusion is that
Now we know that the 9 digits are splitted in 3 groups
It now remains to form the three factors by picking one digit in each group.
Using a similar reasoning
As a result, the three factors formed for the three groups are such that
2
We can calculate:
$
(a*100 + b*10 + c)*(d*100 + e*10 + f)*(g*100 + h*10 + i)= \\
= adg1000000 + (adh+aeg+bdg)100000 + (adi+aeh+bdh+afg+beg+cdg)10000 + (aei+bdi+afh+beh+cdh+bfg+ceg)1000 + (afi+bei+cdi+bfh+ceh+cfg)100 + (bfi+cei+cfh)10 + cfi
$
If we now maximise coefficients in order:
$max(adg)$
a = 9
d = 8
g = 7
$max(adh+aeg+bdg) = max(72h+63e+56b)$
h ...
0
By simply trying out a couple of combinations, I found:
Some of the other combinations I tried are:
My methodology:
Edit: FYI, I did the calculations by hand, rather than with a program, so I didn't try all options.
15
The answer is:
Here's the intuition:
Finally, here's
1
Building on the answers by Elias and CiaPan... Elias gave this "binary search"-based answer.
But it's interesting to notice that we can also do it with this "unbalanced binary search":
Or even like these:
Or the two solutions with the red piece on the outside, which I'm too lazy to draw out.
I don't know if there are other solutions. I actually asked ...
6
I used a nonlinear optimization solver, with variables $x_i$, $y_i$, $w$, $h$. The problem is to minimize $w\cdot h$ subject to:
\begin{align}
i \le x_i &\le w - i &&\text{for $i\in\{1,\dots,12\}$}\\
i \le y_i &\le h - i &&\text{for $i\in\{1,\dots,12\}$}\\
(x_i - x_j)^2 + (y_i - y_j)^2 &\ge (i + j)^2 &&\text{for $1\le i&...
8
Work in progress (may not be optimal)
Picture:
Diagram of contacts:
Coordinates (unconstrained circles at reduced precision):
11
Improved answer
This is similar to another answer but with a smaller area. I worked it out completely independently, then noticed its similarity. The 3" dish is in a different place, and it is not an adjustment based on that answer. It was generated by a C program I wrote for this purpose. It gave my previous answers and has been spitting out smaller ...
6
My answer is
Because
3
What's the par on this course? I can do it in
moves. My strategy is to
Here's the Lichess link: Link
And also, here's the PGN for the answer. Note that black has only one legal move in the beginning - Kh7, and that is where the PGN starts:
Top 50 recent answers are included
