16
votes
Accepted
14
votes
Accepted
an esoteric matchbox
Using the same equation (as other answers), by moving
Second attempt: I have moved
First attempt: I have moved
- 13.6k
10
votes
9
votes
Accepted
8
votes
Accepted
Shuffled binary numbers version 2
First string:
Next, note that
Next, there's only one way
By the same argument,
Now, we can finish things off:
Second string:
Next, let's look at:
Next let's guess that
We can now place
Now ...
7
votes
Accepted
Fitting snakes in a cage
The number is
Example, thanks @Magma for the nice picture:
Proof of minimality:
The snake heads delineate 15 nonempty horizontal subrows. Indeed, there are 5 rows with two and one row with one head ...
- 19.1k
6
votes
Accepted
6
votes
4
votes
Accepted
Is my solution to a mathematics puzzle I created the most efficient solution there is to it?
Let's see what an optimal path would look like. For starters,
- 8,184
4
votes
Accepted
Minimum function optimization puzzle #3: 3 functions
The minimum number of steps is
With the sequence
My approach: work backwards from the goal.
The final step must be
Apply the inverse of h(x) repeatedly and look for values that are near a square.
...
- 13.2k
3
votes
3
votes
The Diamond of Columbus
@DanielMathias found an answer first, but this also fits:
Turns out, after a bit of research there are actually 8 solutions, as seen here:
- 56.4k
3
votes
Accepted
2
votes
Minimum function optimization puzzle #3: 3 functions
A short program in R confirms @DanielMathias answer.
You can try the code here.
The code in text: (not showing correctly because of characters '<' and '>')
...
- 6,155
1
vote
Accepted
1
vote
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