# Tag Info

### Escape from the magic prison

After looking at the problem, I think this problem resembles the "expectancy" problem in mathematics. And this is my way of solving it: 3 + 9 + 27 = 39. You need at least 39 moves to ...
• 1

### Escape from the magic prison

Upper Bound = 36 These were found using a Depth-First Search with pruning. $36$ presses: ...
• 2,203
1 vote
Accepted

### Smallest square with pentominoes

Smallest rectangle with pieces having fixed orientation:
• 16.8k

### What is the least number of colours Peter could use to color the 3x3 square?

As described in many answers, five colors is the minimum. Here we bring in the theory of pandiagonal Latin squares to show some hidden features of the solution and allow a generalization to $n×n$ ...
• 1,080

### What is the least number of colours Peter could use to color the 3x3 square?

Basically a beginner here. Start with a diagonal. All three cells must have unique colours: Then, the two unshaded corners must be given unique colours because both of them have a diagonal with the ...
• 544

### What is the least number of colours Peter could use to color the 3x3 square?

I got by "coloring" with numbers:

### Escape from the magic prison

I've reworked my code entirely in an attempt to find an optimum via A* search. I'm done encoding the worlds and simulation of moves, but I've yet to find a suitable heuristic. My current heuristic is ...
• 3,278
Accepted

### What is the least number of colours Peter could use to color the 3x3 square?

The minimum is because
• 28.2k

### What is the optimal number of function evaluations?

I will ignore the fact that the function is convex. I suspect that this fact doesn't help the worst-case performance. Definition Let $x_{answer}$ be the value of $x$ which for $f(x)$ is minimal. Game ...
• 2,203

### What is the optimal number of function evaluations?

I believe the minimum is Strategy Explicit: Example
• 9,421

### What is the optimal number of function evaluations?

I think the answer is: Order of queries: Let's analyze this below. Let $1\le x_m\le 200$ be such that $f(x_m)$ is minimum. The only way to tell if $f(x_m)$ is minimum is that: Also, if we currently ...
• 958

### What is the optimal number of function evaluations?

I will provide an easy approach (but I don’t think this is the optimized one). After discussion with @thisIs4d I realized that my approach is wrong, but I don't have a better way to improve it for ...
• 760

### Escape from the magic prison

The best upper bound I've found is 39. Here are a few sequences which should solve every possible configuration: ...

### Largest prime number with +, -, ÷

I believe the answer will be obtained through Note that
• 3,633

### Escape from the magic prison

I thought I'd throw my solution into the transporter as well.

### Escape from the magic prison

Step 1. As Jaan Scherphuis pointed out, this step does not take into account that the "winning" combination might not be started from the correct room, thus rendering the entire solution ...
Accepted

### Largest number possible with +, -, ÷

Is there anything in the rules preventing us from simply doing ?
• 7,735

### Largest number possible with +, -, ÷

I can currently do This is achieved via
• 3,640

### Maximizing the common value of both sides of an equation (part 2)

Here is my attempt:
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### Escape from the magic prison

I cobbled together a Python script to test Tim's ideas, with some added insights: I still don't guarantee optimality, because That being said, following the strategy set out in the code gives an ...
• 3,278
Accepted

### Maximizing the common value of both sides of an equation (part 2)

We can do which is pretty large, indeed. If I'm getting the (rather tricky) maths right the value is between
• 7,735

### Escape from the magic prison

Edit: Yes, I am missing something. After it was explained in the comments, I understand what I'm missing, but I'm going to leave this answer so others can learn from my mistake. Since I know it's ...

### Maximizing the common value of both sides of an equation (part 2)

Here are my attempts: which is between
• 1,497

### Escape from the magic prison

This is probably an extraordinarily weak bound, but to get things started, I claim that we can guarantee to get out in no more than To achieve this bound, observe that Now, to find the strategy ...
• 3,640

### Maximizing the common value of both sides of an equation (part 2)

Pretty sure you can get a lot bigger than this, but.. which is
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### Maximizing the common value of both sides of an equation (part 2)

Sorry I missed the fifth arithmetic operation --- power, and thanks for @franck vivien's advice! Here is my update: And, as a supplement, in order to see the order of magnitude comparisons...
• 760
Accepted

### Rest for three days before the next game

Lower bound: Proof positive:
• 16.8k

### Rest for three days before the next game

3,4,5,6,7,8 all have a problem: if 3 is the N: when after the first match 3 days will be lost because the other team would have no competitor... and putting 3 on equation we get 3 days so 3 is ruled ...
Accepted

### Maximizing the common value of both sides of an equation

We can do which equals
• 7,735

### Maximizing the common value of both sides of an equation

This is a small improvement on franck vivien's answer. If you upvote this, please also upvote theirs. The equation has value

I can do With
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I can do with
• 5,096
1 vote

### A variant of the 2-Chess Games overlapped

Note: I assume the discarded kings to be exempt from the no-collision rule. Game 1: Game 2: I do not claim minimality. Overlay Game 2 pieces circled:
• 7,735
Strategy We already have a computer solution, so I will try to show how a human can obtain it. The strategy is to set the numbers $1,2,\dots,9$ on the anti-sudoku grid one by one. Let $A$ be the ...