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 ...
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

Find the perimeter (seemingly unsolvable problem)

Yet another proof without words:
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
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 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
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

Find the perimeter (seemingly unsolvable problem)

A visual solution, without so much math:
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 ...
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 ...

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