New answers tagged number-theory
6
Here is a solution with a constant product of
which I think is the minimum possible:
Some partial progress for a lower bound on the product:
This leaves only a few possibilities for improvement:
3
I found a solution trying to minimize prime factors. And finding a balance between the minimum value and minimum number of factors.
I noticed that some fields are connected, in that multiplying one of them results in the multiplication of fixed other fields. There are three such patterns:
-C, D, H, L, and M (and any mirror image of that)
-A, E, G, L, M (...
6
Edit: In an effort to find the minumum, here is a much smaller solution in which the mutual product is
Solution
As MKBakker pointed out we could further reduce this by dividing each of the entries 4,8,16,96 and 192 by 2 to get a mutual product of
although they have subsequently improved on this.
14
There are a number of ways to do this. An easy strategy:
9
To do this,
Finally,
I can give you the Python code if you want. Not sure it can be spoilered (I've never learned how to have multi-line spoilers).
Python Code
5
Then,
Additionally,
3
However
Why?
so whatever Bob can arrange these cards in the best case scenario,
Let's make it more complex;
so even it is 0 to 100, Ann will
1
To formalize user61579's answer, a simple reinterpretation of the rules is that, defining a pass as a move from the $1$ all the way around the sequence, every pass, every second $-1$ becomes $0$
Then, it is trivial to show that the state of a length-n sequence after each pass corresponds to the first n columns of this infinite table:
1 -1 -1 -1 -1 -1 -1 -1 ...
4
Code to find the pattern: https://ideone.com/O5S4Qu
(The third number printed out on each line is the winning move if the player to move is in a winning position)
3
We have a winning strategy for:
The first move is:
2
For the first question, there is an easy pattern that we can detect. First, all of the nice jumps will come from the n-1 position for an array of length n.
As for how many, I'll print the first few and then try to point out the pattern
2: 0
3: 0
4: 1
5: 0
6: 2
7: 1
8: 1
9: 0
10: 3
11: 2
12: 2
13: 1
14: 2
15: 1
16: 1
17: 0
2 and 3 are basically special ...
7
Here's a little Python program to test it yourself:
https://repl.it/repls/ScientificIdenticalPixels
And here's C++ code written by user @im_so_meta_even_this_acronym
https://ideone.com/SfMHqC
Top 50 recent answers are included
