129
votes
Accepted
A man possesses a large quantity of stamps
For the more visually inclined, arrange all positive integers in a 5-wide chart, as follows:
...
- 2,245
56
votes
Accepted
55
votes
Accepted
Is this chromatic puzzle always solvable?
Yes, it's possible.
Start with the various 2x2 squares.
Ignoring symmetries of rotation and color swapping, there are 1 combination of 1 color, 3 combinations of 2 colors, and 2 combinations of 3 ...
- 7,438
49
votes
Accepted
Pirate democracy at its finest
I have a hunch that the answer is
Explanation:
Continuing this way, we see that
- 27.9k
48
votes
48
votes
Accepted
All numbers in a 5x5 Minesweeper grid
Assuming standard Minesweeper rules, here’s one solution (with $ X $ = a mine):
EDIT: In response to Euphoric in the comments, I solved this purely by logical deduction with a bit of educated ...
- 16.3k
48
votes
Accepted
43
votes
Accepted
43
votes
Accepted
41
votes
Transferring 9 pegs on a 9x9 grid
I was having a slow work day, so I fired up Blender and made this:
In 13 hops, the block of 9 pegs can be moved two places down and to the right. By repeating the process two more times, the pegs can ...
- 9,621
39
votes
Accepted
36
votes
Accepted
Dominos on a checkerboard
Looks like:
Thanks to @Gamow's comment, this number's maximality can be proved
by self-contradiction of the assumption that it is not maximal.
Any more dominos would cover all 64 squares.
Assumption ...
- 21.8k
34
votes
Accepted
34
votes
Two out of a dozen cartons have Easter eggs. Two people try to find one Easter egg carton, each using a different strategy. Who is expected to win?
(context: note that this question is asking for intuitive explanation why it's not equal, so a good answer would have to explain intuitively why the intuition that they will be equal is not the right ...
- 5,632
32
votes
Accepted
31
votes
Accepted
Creating the hardest 6x6 maze
I can make the robot take
The robot must take this many steps because
- 5,461
30
votes
Accepted
Do Langford squares exist?
Langford squares are not possible.
Consider the middle two rows of a $2n \times 2n$ Langford square. They, like all rows, must contain $n$'s. Any $n$ must have a partner $n$ in its column that's $n+1$ ...
- 26.3k
28
votes
28
votes
Accepted
Tiling a rectangle with nine squares
The dimensions are
and the tiling looks like this:
Working out the dimensions of the rectangle is quite easy. We know its total area is $4209$ (i.e., $2^2 + 5^2 + 7^2 + 9^2 + 16^2 + 25^2 + 28^2 + 33^...
- 9,621
28
votes
Accepted
28
votes
Accepted
Perfect Golomb Circles
Complete first answer:
Yes there exists one for order 5. Consider the combination $1,3,10,2,5$.
Partial second answer:
A perfect circle of order 98 :
$$1, 2, 34, 15, 139, 117, 24, 101, 481, 5, 65,...
- 1,161
27
votes
Accepted
Professor Halfbrain and the fantasy knight
Yes there is a solution with a very simple strategy:
Start in (1,1).
Always go the right most square that's unvisited
I'll try to illustrate it. I checked it by hand on an 9x9 board and a very nice ...
- 11.2k
27
votes
Accepted
The frog concerto
The answer is
This is because
Now, to calculate the position for 24 frogs, I broke it up into 2 parts:
Therefore
- 7,540
27
votes
Accepted
Averaging numbers on the blackboard
First choose $2014$ and $2016$. Average = $2015$. Now take the $2015$s. Their average is $2015$.
Now choose $2015$ and $2013$. Average = $2014$.
Choose $2014$ and $2012$. Average = $2013$.
Note ...
- 1,348
27
votes
Accepted
Salesman's claim for mechanical keypad lock - 5 buttons and 545 combinations!
Using only combinations of either single or double button presses:
Using 1 press
Using 2 presses
Using 3 presses
Using 4 presses
Using 5 presses
Total
For anyone curious as to my internal ...
- 394
27
votes
Accepted
France's Public Holidays' Puzzle
First of all,
It will probably make a difference
So let's concentrate on the other ones
We can already stop here;
so
- 27.9k
27
votes
Winning Strategy for the Magician and his Apprentice
Here is a simple strategy of how they could do it
Proof
- 133k
27
votes
Accepted
Controlling a robot blindfolded on a 9x9 grid
My first attempt was done by hand. It used 28 commands:
but this was not optimal. I have now done a computer search to find optimal solutions.
It found 180 solutions of length
No shorter solutions ...
- 50.8k
26
votes
Tommy's Train Tracks
Let's think of each piece not as curved but as an L shape, with two sections at a right angle. Adjacent pieces in the track join in a straight line. If we pair off the touching sections, we see the ...
- 26.3k
Only top scored, non community-wiki answers of a minimum length are eligible