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3 votes

Split a number in half, sum it, square it and get the number back

We are looking for $2k$-digit numbers $N^2$ such that adding their first half to their second half yields $N$. This implies that it would be better to turn our attention to $N$ itself. And here are ...
AxiomaticSystem's user avatar
9 votes

Split a number in half, sum it, square it and get the number back

daw's (now deleted) answer contains a good starting point. Namely: Now, Let's apply some elementary number theory: Take the intersection of two results and we get resulting in the answers For 2-...
Bubbler's user avatar
  • 15k
4 votes

Split a number in half, sum it, square it and get the number back

The math way (added second) Let's say k is the number of digits... Write the equation like $ (x + y)^2 = 10^{\frac{k}{2}} x + y $ Transform this to a quadratic equation and try to find y based on x $ ...
Marius's user avatar
  • 18.1k
7 votes
Accepted

Keys and Locks Puzzle

The exact condition is Actually, something slightly stronger is true: A strategy is winning if and only if We can prove this equivalence by an application of Suppose we are handed any strategy. ...
Tim Seifert's user avatar
  • 1,116
4 votes

Keys and Locks Puzzle

I thought of it in terms of a Suppose Can this always be done?
Tyler Seacrest's user avatar
11 votes

Keys and Locks Puzzle

I believe the condition is: This condition is sufficient. Is this condition necessary?
Florian F's user avatar
  • 30.6k
5 votes
Accepted

Current record for minimally clued 7x7 Hidato (16 clues)

Solution: Step by step: 1: 2: 3: 4: 5: 6:
Beastly Gerbil's user avatar
0 votes

Oh no, my chocolate banana puzzles are not unique!

Let's get this ball rolling. Basic deductions: Any cell with a 1 or 2 is shaded. Any cell with a number that has a prime factor larger than the side of the grid in not shaded. Any cell which is ...
ralphmerridew's user avatar
9 votes
Accepted

Create an empty 8x8 One Up puzzle with a unique solution

Actually I found a solution to this question shortly after I posted this answer. Puzzle: Solution: Solving path: This is an extension of the second "connected 3x3 One Up with unique solution&...
Bubbler's user avatar
  • 15k
8 votes

Create an empty 8x8 One Up puzzle with a unique solution

I think this grid works: It's not hard to see how all the entries are forced leading to a unique solution. Final grid: This generalizes to square grids of any size 3-by-3 and up (2-by-2 is ...
xnor's user avatar
  • 27k

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