# Tag Info

## Hot answers tagged algebra

Accepted

### The numbers on blackboard

Let $$f(a,b) := \frac{\sqrt{a^2+3ab+b^2-2a-2b+4}}{ab+4}.$$ John's procedure is now to repeatedly replace the leftmost two values $a,b$ on the blackboard by the single value $f(a,b)$. I claim that John ...
• 5,364
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### Two Cannons - A Beginner's Physics Puzzle

Alain Remillard has given the mathematician's answer. Here's the physicist's one: Step 1: Obviously, in such a universe, regardless of their speed, the cannonballs will travel in a straight line and ...
• 78.1k
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### Google cannot find me

Okay so I think the answer is Google cannot find me, reflected I'm lemon and lime, googling 'me' is when you fall, me and meme will answer all.
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It is Reasoning:
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### Programmatically solving a math puzzle with four unknowns and four equations

First of all, let's see why your brute-forcing fails. (This is the puzzle part, the rest is plain old math.) No matter which you chose, the number at the bottom right would have to be both odd and ...
• 78.1k
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### Vector Sum of Pythagorean Triples

The graph of real-valued Pythagorean triples $x^2+y^2=z^2$ forms an infinite cone if we restrict to $z>0$: A sum of $n$ independent vectors on this cone is $n$ times their average, which lies ...
• 27.4k
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### Big number puzzle

And here is the number you are probably thinking of: It works only for $ab$ where $a \le b$. I suppose that it is a mistake in the problem statement. Others have proven that as it is, the problem ...
• 30.9k
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### Can you find the number?

The number is because we can rewrite the three given conditions as follows, where $H$, $T$, and $U$ are the hundreds, tens, and units digits respectively: Adding the first two gives Also from the ...
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### Which is larger? $\sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2}$ versus $5$

Here's another approach, which starts from smaller integer residuals than hexomino's solution. and Finally, bringing these lines of argument togegther, I admit it isn't a single chain of inferences....
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### A packing game!

With the following arrangement you can easily stack pieces into the box: I have assumed without loss of generality that $a<b<c$, but as Damien_The_Unbeliever noted in the comments, it also ...
• 54.6k
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### Trickier hand tiling

@tom was correct about the size of the squares and the combinations. I tiled them on graph paper shown below. Placing them roughly largest to smallest, trying to avoid leaving small gaps where ...

### Which is larger? $\sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2}$ versus $5$

Yet another method: And then:
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### Balancing the marble game (Red marbles are OP, please nerf)

How can Ash win? Looking at the game tree: Formalising the above, we get the following relationship for $p_A$, the probability that Ash wins: Ash and Bree desire for $p_A = \frac{1}{2}$. ...
• 408
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### The NANNP Grid ( Not another Next Number Puzzle )

So stacking Then the rest So So the four numbers are
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### Inductive or Deductive Reasoning

You just need to reverse the process to get back the original values
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### Cube the digits and carry on

I observed the following: This is because This observation immediately excludes many numbers from consideration. It remains to be shown that the numbers that were not excluded do all end at $153$. ...
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By definition of (Euclidean) length, 2-dimensional vector $v_j:=(a_j,b_j)$ has length $|v_j|=c_j$ if and only if $a_j^2+b_j^2=c_j^2$ ($c_j\ge 0$). By repeated application of the we have for any ...