# Tag Info

## Hot answers tagged mathematics

Accepted

### Starting with 2014 "+" signs and 2015 "−" signs, you delete signs until one remains. What’s left?

Notice that, if you set + = 0 and - = 1, then the mod 2 of the sum does not change under either transformation. Hence, the final sum must be equivalent to the original sum, 2015, mod 2. Therefore the ...
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### What is the least number of colours Peter could use to color the 3x3 square?

The minimum is because
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### Starting with 2014 "+" signs and 2015 "−" signs, you delete signs until one remains. What’s left?

Now that an officially new user has answered let me remark that + and - cry out to be read as and the entire thing can ...
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### 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 ...
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### Starting with 2014 "+" signs and 2015 "−" signs, you delete signs until one remains. What’s left?

I think this answer is equivalent to BlazingSnow's answer, but instead of assigning numbers to the symbols and then reducing mod 2, I do a case analysis and observe parity of the count of each symbol: ...
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### Unorthodox angle measuring device

The device is a: Then: This device also fits the three hints:
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### Getting lost on a Circular Track

For the non-zero segment size: For the zero segment size case:
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### 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: ...
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### Guesstimate a multiple choice exam

Unless I got tricked, because
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### Escape from the magic prison

Upper Bound = 36 The best result was found using a Depth-First Search with pruning. $36$ presses: 111233233311312321212131213231313222 $37$ presses: ...
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### Getting lost on a Circular Track

For the single-point exit, you can't do better than @fljx's answer. Watch out, because:
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### 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 ...
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### Manhattan distance

The place to start is: Now let us place: Moving down the chain: And the next: You guessed it: Finishing up:
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### The subtraction game

This is (surprisingly) actually a win for Alice! If she chooses [9, 5, 4, 11, 6, 14, 3, 8, 15, 12, 18, 7, 16, 24, 13, 36, 63, 48] she is guaranteed to win for any number greater than 96. Using the ...
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### 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 $n×n$ ...
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### Starting with 2014 "+" signs and 2015 "−" signs, you delete signs until one remains. What’s left?

We can delete any two symbols so order doesn't matter, it suffices to track the counts: let p, m be the number of plus and minus symbols. We have three kinds of ...

### Getting lost on a Circular Track

It might take awhile, but we can get out.
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### 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 ...
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### Combination lock on a pentagonal rotating table

My procedure is: For the proof, first some setup ignoring the rotations: The main claim: Now to address the rotations: To prove the claim, Other thoughts:
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### Manhattan distance

Since someone beat me to it, I won't post the solve path, but only the key observation, that The solve is easiest if you and the full solution is
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### What is the least number of colours Peter could use to color the 3x3 square?

I got by "coloring" with numbers:

### Starting with 2014 "+" signs and 2015 "−" signs, you delete signs until one remains. What’s left?

Straightforward thinking: There are three ways to remove two signs: Remove two +s, then add one back (effectively removing one +...
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### 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 ...
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### 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 ...
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### Unorthodox angle measuring device

I'm not really sure about the precision/accuracy but I think this could be on the right track. If not the correct method, then at least that it's related to the If we convert the first term in each ...
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### Visual puzzle involving mathematical operations

I’m not sure if there exists some kind of coincidence, but I noticed… step 1. add up the numbers with the same color of each row/ column  \begin{array}{cc|ccccc} row/col & value & orange &...
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### Everyday words for terminology

Here's my attempt. I think a few are shaky, but it's plausible. First group: Second group: Third group: And finally:
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