# Tag Info

### 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 ...
• 10.9k

### 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-...
• 15k

### 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 \$ ...
• 18.1k
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. ...
• 1,116

### Keys and Locks Puzzle

I thought of it in terms of a Suppose Can this always be done?
• 9,459

### Keys and Locks Puzzle

I believe the condition is: This condition is sufficient. Is this condition necessary?
• 30.6k
Accepted

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

Solution: Step by step: 1: 2: 3: 4: 5: 6:
• 59.7k

### 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 ...
• 4,332
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&...
• 15k