122
votes
Is this Hashi puzzle unsolvable?
Here is another argument for why this puzzle is unsolvable.
The Handshaking Lemma is the simple but powerful idea that each edge uses up a value of 2 (one from each end), so the total amount must be a ...
- 50.8k
48
votes
Accepted
Is this Hashi puzzle unsolvable?
There is no solution (see diagram).
First, the 8-island must be connected as indicated.
Second, the 1-island in the top row must be connected as indicated.
Third, the 3-island in the top row must be ...
- 5,878
43
votes
Accepted
Are there seven consecutive annual dates which result in Monday-Sunday?
Yes
So
Example sequence:
- 10.3k
34
votes
If A cents can be paid with B coins then prove that B dollars can be paid with A coins
The reason it works for this set of coins is that
Using this fact, you can look at each coin value individually:
Since the statement is true for each coin value, it is also true for any combination ...
- 50.8k
32
votes
27
votes
Accepted
An Infinitude of Deceptive Devourers
Answer:
Explanation:
Consider two possible cases.
Case 1 - the children used the "at least" convention:
Let's consider two subcases.
Case 1a - only a finite number of people ate cake
Case ...
22
votes
Accepted
Do you know where your number ranks among your peers?
I tried this problem without looking at the answers first. But I came to a different conclusion to the other answers. So I'm posting another answer here.
The answer to the question is
We can ...
- 436
19
votes
Accepted
The Metaslitherlink
Answer:
Let's first solve the small slitherlinks:
For most of the small slitherlinks I think I know what they mean:
And I think this could be the final answer:
- 4,834
19
votes
How do I determine whether a 5x5 Lights-Out puzzle is solvable without trying to solve it?
To test if a 5x5 Lights Out pattern is solvable, you need to check two things. First look at the top, middle and bottom rows, at the first two and last two lights - the 12 lights bolded here:
[1, 0, ...
- 50.8k
18
votes
Accepted
18
votes
Accepted
18
votes
Accepted
A Trivial Pursuit #12 (Sports and Leisure 2/4): Logic Boat
The 6-letter word that can be extracted is:
The solution path:
- 14.2k
18
votes
Accepted
A Trivial Pursuit #25: Meta-Analysis
The overall answer is a very fitting trivial pursuit:
Or is it 20 words? (Or does the hyphen make it 21?)
Which happens to be the
How did we get here? Many probably saw this outright but I was ...
- 24.7k
17
votes
160 foxes are stuck on an island with 1 chicken. Will the chicken be eaten?
Let's start with a different scenario:
Now,
Therefore,
However,
I'm beginning to see a pattern here:
Therefore, in our original scenario with 160 foxes,
- 9,597
17
votes
What technique can be used to solve this 6x6 sudoku?
You can do sudoku to
That will eventually place the same digit in a spot where a three cannot go:
After that deduction, the grid will basically fill itself.
The technique that finds relationships ...
- 76k
16
votes
Accepted
Can experienced players tell when a Sudoku was randomly generated? Or if it's a shuffled version?
Can you tell when a puzzle has been computer-generated?
Yes, absolutely. Handmade puzzles can very easily be distinguished from computer generated ones by their "solve paths", and often ...
- 145k
16
votes
Accepted
16
votes
Accepted
15
votes
Accepted
15
votes
Accepted
Two Doors and a Guard
Consider the following possibilities for heads 1 and 2 respectively (where T is a truth-teller and L is a liar).
So you can ask
and who ever answers
- 13.7k
15
votes
Accepted
If A cents can be paid with B coins then prove that B dollars can be paid with A coins
[An attempt to make an intuitive answer]
[Based heavily on the other answers by Jaap and Plop]
Chat asks what happens if we swap the 20c coin for a 25c coin.
so it is less obvious that it holds, but ...
- 270
15
votes
Accepted
14
votes
Accepted
14
votes
Accepted
14
votes
Accepted
Where to start with a large crack the lock puzzle like this?
The main thing you need to know to solve this puzzle is that
[Solution path below]
Furthermore,
Notice now that
- 8,307
14
votes
Accepted
13
votes
Accepted
PSE Advent Calendar 2022 (Day 20): The Christmas Gift
Bob wants
We can start by looking at
We can now complete the bottom half of the nongram by simple deductions:
Continuing up from the bottom we get a hint of blue!
We can now complete some columns ...
- 56.4k
13
votes
Accepted
13
votes
Accepted
A Trivial Pursuit #19 (Geography 4/4): Glass
The five-letter word we're looking for is
To get there, we must first
As for the flags, those represent
So now we have our menu. Now what to do with the graphic?
Finally, to extract the answer,
...
- 9,597
13
votes
Accepted
PSE Advent Calendar 2023 (Day 3): 24 dangerous doors
Solved grid:
It was fun!
General solve path:
- 5,632
Only top scored, non community-wiki answers of a minimum length are eligible