38
votes
Find the perimeter (seemingly unsolvable problem)
Here's a non-visual solution which some may find more easy to understand than a visual solution:
- 2,165
30
votes
Find the perimeter (seemingly unsolvable problem)
To me the most visually intuitive solution is as follows:
First of all,
Then take
- 13.8k
11
votes
Find the perimeter (seemingly unsolvable problem)
the answer is
here is the solution;
sorry for my handwriting :D
- 29.3k
11
votes
Find the perimeter (seemingly unsolvable problem)
An intuitive solution:
red is 15, blue 9, green 12
Perimeter is 2 x (red + blue + green) = 72.
In each of two steps rotate the highlighted bit of the perimeter by 180 degrees.
Variation:
The same ...
- 14.8k
11
votes
Find the perimeter (seemingly unsolvable problem)
A principled solution:
The perimeter length of
follows from the following
Theorem:
Let P be a polygon with only right angles. Then the sum of all up facing sides equals the sum of all down facing ...
- 3,437
9
votes
A series of rock-paper-scissors games
If my friend is playing without a strategy, the best approach would be
Note: I imagined that they were playing a rock-paper-scissor card game because the number of possible outcomes for my friend's ...
- 29.3k
9
votes
1000 digit sum calculation puzzle
Verification:
To find alternatives, we need use the following insight:
In this particular case that means
Now let's use that fact to find an alternative set. Suppose we try to change the first ...
- 46.7k
6
votes
Accepted
A series of rock-paper-scissors games
Initialise $p_{rock} = \frac{40}{100}, p_{paper} = \frac{35}{100}, p_{scissors} = \frac{25}{100}$.
Choose the opposition attack which destroys their most probable option.
So, best option to win in ...
- 166
5
votes
4
votes
Find the perimeter (seemingly unsolvable problem)
If we want to find the sum of all the vertical sides we have 15 and the other vertical sides on the right all add up to 15, giving us a vertical sum of 30. But if we want to find the horizontal sum, ...
4
votes
Accepted
Detecting Connected Components on an Infinite Graph after Modification
The original graph
Suppose we want to know whether vertices A and B (after finitely many known additions and removals of edges) are connected. Then:
Now
So
- 114k
4
votes
A series of rock-paper-scissors games
The randomness of the sequence must be more clearly defined to provide an answer.
My first thought was like the answers of Oray and gsomani. However, this assumes the following randomness rule be ...
- 4,344
4
votes
1000 digit sum calculation puzzle
First part is quite easy to verify:
2nd part is another story....
After some computing, we found that we can replace every number by
Some others solutions
- 882
3
votes
Find the perimeter (seemingly unsolvable problem)
An easy way to solve this is to just let the overlap be 0. Since the overlap could be any length, WLOG, we might as well let it be 0. Then the vertical sides sum up to 30 and the horizontal sides sum ...
2
votes
2
votes
1000 digit sum calculation puzzle
Let the numbers be $N=\{a,b,c,d,e,f,g\}$ where $\max(N)=g$. We impose
$$S_\text{left}=a+b+c+d+e+f+g=\sum_{i=0}^\infty\mathrm{mod}\left(\frac{abcdefg}{1000^i},1000\right)=S_\text{right}.$$
Now $S_\...
- 121
1
vote
100 prisoners and a secret number (potential solution)
Your answer assumes that each prisoner hears the numbers that were guessed by the previous prisoners. How else could they "guess 1 less than the previous prisoners guess". This is ruled out ...
- 46.7k
1
vote
Detecting Connected Components on an Infinite Graph after Modification
It turns out that we can mostly ignore finiteness or lack thereof since the relevant feature, the unique connecting path between any two vertices, is always finite.
Let's look at removals of edges ...
- 14.8k
1
vote
Island of Liars
Note one very important thing that has been mentioned, "he found out he had all the numbers from 0 to 956 typed in uniquely". This means that no two people said the same number. Also, since ...
- 1,930
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