12 votes

Four-cornered cow inheritance

Following spherical-wug-in-a-vacuum's basic approach, what about Following the old The Sheik Dies puzzle, That may imply that
Tyler Seacrest's user avatar
9 votes
Accepted

Pythagorean pentagons

Here's another possible solution, without flipping:
Edward H's user avatar
  • 1,038
8 votes

Divide rubies and diamonds on a necklace into 2 equal halves

Note that: Edited to add illustrations:
SQLnoob's user avatar
  • 7,972
7 votes

Pleasant Cuboids

We are trying to find positive integer solutions to $xyz = 2(x-2)(y-2)(z-2)$. First I'll establish some bounds. Lower bound: Upper bound: Now we can check the few cases for $x$:
Jaap Scherphuis's user avatar
4 votes
Accepted

A functional equation: Composition to get a... linear function?

Sure, let $$f(x) = \sqrt{2}x+4(\sqrt{2}-1)$$ I found this by assuming $f$ has the form $f(x)=\sqrt{2}x+c$ to get the $2x$ term in $f(f(x))$, and solved for which $c$ gives $+4$. We could have also ...
xnor's user avatar
  • 26.6k
3 votes

Four-cornered cow inheritance

This can imply that This part of the problem can imply that Thus, we can find: But
spherical-wug-in-a-vacuum's user avatar
3 votes

A functional equation: Composition to get a... linear function?

We can also create piecewise linear solutions. For instance, consider the following function: Let $n$ be the largest power of two smaller than $\frac{|x+4|}{3}$. If $\frac{|x+4|}{3n} < \frac{5}{3},$...
isaacg's user avatar
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3 votes

Pleasant Cuboids

I think Weather Vane has identified all the cuboids. Here is a method to mathematically narrow down your options for $x,y,z$ to a finite range
hexomino's user avatar
  • 135k
2 votes

How to make 2012 by using 2, 0, 1, 2?

My approach relies primarily on the Primorial and Multi-factorial operations. To simplify and make it easier to read, I am using the notation P(n) to represent the primorial of n. Feel free to let me ...
TLE on test 77's user avatar
2 votes

How to make 2012 by using 2, 0, 1, 2?

A shortened version based on @hexomino's nice solution: I don't understand why the ceiling function is allowed, but why the floor function should not be allowed. If it is allowed you could shorten it ...
theozh's user avatar
  • 1,639
2 votes

How to make 2012 by using 2, 0, 1, 2?

Here is another possibility Hence
ThomasL's user avatar
  • 11.9k
2 votes

Divide rubies and diamonds on a necklace into 2 equal halves

Here is how to do.
Florian F's user avatar
  • 28.4k
2 votes

Pleasant Cuboids

I have found
Weather Vane's user avatar
  • 14.3k
1 vote

Pleasant Cuboids

The puzzle technically asked for just the number of cuboids. So in my approach, I emphasize simply counting the solutions rather than listing them. As discussed elsewhere, the governing equation is $2(...
Oscar Lanzi's user avatar
1 vote

Getting The Numbers 33 Through 99 Only Using 2, 0, 2, and 4

I'm assuming we can use exponentiation, factorial, and N-th root operations Here are my solutions so far --> (Sorry for the bad formatting!) I haven't figured out the answer for the numbers with ...
TLE on test 77's user avatar
1 vote

Four-cornered cow inheritance

Note that... Also, I'm curious if we're misusing the word "cow", or if this ranch really has no bulls? (Or are the bulls not part of what's being divided?)
Matthew's user avatar
  • 367
1 vote
Accepted

Place numbers 1 through 9 in boxes (☐☐×☐=☐☐+☐☐=☐☐)

I would focus on the single digit number
Retudin's user avatar
  • 8,274

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