# Tag Info

### What is the maximum number of people who speak only 1 language?

I believe the answer is Intuitively, we would achieve the maximum number of people speaking only one language by assuming all of the remaining people speak all three languages, so we can set up a ...
• 599
Accepted

• 4,797
Accepted

### Combine 8x8 square grid and 15x15 square grid into 17x17 square

Here is a solution where the number of pieces is I believe that fewer pieces is not possible, but do not have proof. Here are some observations that might lead to a proof:
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### What is the maximum number of people who speak only 1 language?

A visual explanation:
• 466
Accepted

### Maximizing row and column products in a 4x4 grid

The base question is rather straightforward: The maximal power of 2 that divides the product of numbers up to 16 is 8 + 4 + 2 + 1 = 15. Because there are 4 rows and columns, it's clear that the ...
• 599

### When Beatrix stops placing dominoes on a 5x5 board, what is the largest possible number of squares that may still be uncovered?

Another way to do the proof of optimality: Could there be a domino here?
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### When Beatrix stops placing dominoes on a 5x5 board, what is the largest possible number of squares that may still be uncovered?

The answer is Proof of optimality:
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### What is the maximum number of people who speak only 1 language?

You can solve the problem via integer linear programming, with a nonnegative decision variable $x_S$ for each of the seven nonempty subsets $S$ of the three languages and linear constraints to enforce ...
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### Shortest Algorithm to flip 2 edges on a Rubik's cube

I found an MU 2 flip that's 12 moves long and flips the DF and UR edges, which is much easier to execute than an MUF one. It goes M U' M U2 M' U' M' U' M' U2 M U'. When executing the M moves at the ...
• 31

### Flea in six boxes

Case 1: Case 2 is surprisingly simple: Case 3:
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### Weigh 15 boxes with a digital scale, but you canâ€™t understand the number system

It can be done in: Step 1: Step 2a: Step 2b: Step 2c: Step 2d: Step 2e: Step 2f: Step 2g: Step 2h:
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Accepted

### Placing dominoes on a 16 × 14 grid

With computer search using Picat, it can be shown that Daniel's solution is the minimum. ...
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### Placing dominoes on a 16 × 14 grid

Not sure if this is minimum, but I can do it with Image:
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Accepted

### Superman looking for Supergirl

We require a lemma: For a given distance $D$ and number of rooms $R = mD+n$, there are $n$ sets of $m+1$ rooms that Supergirl could travel between, and $D-n$ sets of $m$ rooms. Let's begin by ...
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1 vote

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1 vote

### Superman looking for Supergirl

Edit: I misread the problem. I thought it was 1 million rooms, not 100,000. But the approach is still the same. I solved it for 100,000 rooms. The answer is 10,000,000.001 seconds or 3 months, 23 days,...
• 554
1 vote

### Flea in six boxes

Case 3: For a cost 10 solution: There are many cost 10 solutions however: I could not find a (easy) proof that cost 9 is impossible
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1 vote
Accepted

### Weighing Coins -- a Different Approach

We know that $3$ weighings suffice for $13$ coins if we have one known good (see here), so for $4$ we can split $39$ coins into three groups of $13$ and weigh two of the groups against each other. ...
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1 vote

### What is the maximum number of people who speak only 1 language?

Another approach: But to meet constrains, for example:

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