# Tag Info

### 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 ...
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### 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 ...
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### Are there seven consecutive annual dates which result in Monday-Sunday?

Yes So Example sequence:
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### 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 ...
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### The thief, liars, and the honest

Even simpler solution, with no hypotheticals needed:
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### 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 ...
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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 ...
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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:
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### 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, ...
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### Knights and knaves not on an island

Then Beta says, "Frank and I are different types."
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The title suggests The starting point:
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### 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
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### 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 ...
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### 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,
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### 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 ...
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### 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 ...
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### Double Choco: Snaking

First Then Breakthrough Finshing
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### 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
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### 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 ...
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### Playing Mastermind against an angel and the devil

For the angel: For the devil:
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### 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
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### Relatively prime numbers

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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 ...
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### Painting a Checkerboard

The optimum is achieved by Proof of optimality:
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### 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, ...
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