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30 votes
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 ...
Magma's user avatar
  • 5,324
24 votes
Accepted

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 ...
Bass's user avatar
  • 77.7k
18 votes
Accepted

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.
hexomino's user avatar
  • 137k
16 votes
Accepted

Board with all 2020s

It is Reasoning:
WhatsUp's user avatar
  • 7,407
15 votes
Accepted

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 ...
Bass's user avatar
  • 77.7k
13 votes
Accepted

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 ...
xnor's user avatar
  • 27.4k
12 votes
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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 ...
Florian F's user avatar
  • 30.6k
12 votes
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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 ...
Rand al'Thor's user avatar
11 votes

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....
Rosie F's user avatar
  • 8,640
11 votes

Two Cannons - A Beginner's Physics Puzzle

They will I did it mathematically Suppose the horizontal distance between both cannons is $d$ and the up angle from right cannon is $\theta$. Then, the left cannon is at a height of $d\tan\...
Alain Remillard's user avatar
10 votes
Accepted

Videogame salesmen

Edit:
Jaap Scherphuis's user avatar
10 votes

SafeCracker #3 - We've Been Blocked

The doesn't belong, because
19aksh's user avatar
  • 3,943
9 votes

Google cannot find me

Is the answer Googling it returns me and meme will answer all. Can't make the middle two lines fit though
Mohirl's user avatar
  • 5,016
9 votes
Accepted

The special machine

This is probably similar to msh210's idea but if we write
hexomino's user avatar
  • 137k
8 votes

Board with all 2020s

A less technical solution: We can (try to) make a symmetric solution that makes all numbers equal (where the 6 variables signify how often a cell is chosen): ...
Retudin's user avatar
  • 81
7 votes
Accepted

SafeCracker #3 - We've Been Blocked

The odd one out is the This is because Safe Cracked!
Voldemort's Wrath's user avatar
7 votes
Accepted

Houses and Telephone #s

Explanation:
noedne's user avatar
  • 15.4k
7 votes

Big number puzzle

I am going to prove that Indeed Let me dump here previous thoughts that turned out not to be useful but might be in the future. First, Second
Arnaud Mortier's user avatar
7 votes

Triangular conundrum

newbie's user avatar
  • 907
7 votes
Accepted

Whose birthday is it?

Let us denote the ages of Person 1, Person 2, Person 3 by $x,y,z$ respectively. We'll assume that $x,y,z$ are positive throughout. The product of the 1st person's and the 2nd person's ages is $311 \...
hexomino's user avatar
  • 137k
7 votes

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 ...
Jaap Scherphuis's user avatar
6 votes
Accepted

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 ...
QuantumRipple's user avatar
6 votes

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

Yet another method: And then:
Toby Mak's user avatar
  • 494
6 votes

Determine the cost of the book

Answer: Reasoning: If the book has a cost of 'x', Sarah has 's' dollars and Jane has 'j' dollars, the following equations true: x = s + 10 (1) x = j + 1 (2) There's also an inequity we know of: s + ...
Tim Couwelier's user avatar
6 votes
Accepted

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 $p_A = \frac{1}{2}$. ...
infinigon's user avatar
  • 408
5 votes
Accepted

The NANNP Grid ( Not another Next Number Puzzle )

So stacking Then the rest So So the four numbers are
El-Guest's user avatar
  • 32.3k
5 votes

Determine the cost of the book

The book costs:
Dan Russell's user avatar
5 votes

Inductive or Deductive Reasoning

You just need to reverse the process to get back the original values
stack reader's user avatar
  • 9,840
5 votes
Accepted

The Marble Game

Answer:
Lanny Strack's user avatar
  • 6,068
5 votes
Accepted

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 $153$. ...
Jaap Scherphuis's user avatar

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