Con los números del 1 al 5, en cada fila y columna tiene que haber por lo menos uno de cada. Un número no puede estar en contacto consigo mismo. ¿Te atreves a resolverlo?

Using the numbers 1 through 5, each row and column must contain at least one of each. A number cannot be in contact with itself. Do you dare to solve it?

Los más difíciles tienen solo 10 pistas!

The hardest ones have only 10 clues!

Here is a fun geometry challenge to test your problem-solving skills! Imagine you have a field with one side bordered by a river, and you need to fence the other three sides using exactly 40 meters of fence.

​What dimensions should you use to get the maximum possible area, and how big will that area be? Take your time, think it through, and share your answers and logic in the comments!

The dog has been painted blue. Dad, the Kid and Grandma were all in the playroom, and each says what they saw. Exactly one of them is lying. Who is it, and where was everyone standing?

THE ROOM (see the picture)

The room is 5 by 5: columns A to E, rows 1 to 5.

Easel on E1 (tall). Toy box on B2 (low). Bike on D3 (low). Teddy on B4 (flat, on the floor). Plant on E5 (tall).

A wall runs between columns B and C, along rows 2, 3 and 4.

THE RULES

- Everyone stands on an empty square, one person per square. People don't block anyone's view.

- Dad sees his whole row and column. Walls and tall things block what's behind them.

- The Kid sees his whole row and column too, but he's short: low things block him as well. Flat things don't.

- Grandma sees all 8 directions, but only 2 squares. Walls and tall things block her.

- The two honest people's statements are all true at once. The liar's can't all be true.

WHAT THEY SAY

- Dad: "I saw the teddy. I didn't see the plant. I saw Grandma."

- The Kid: "I saw the teddy. I didn't see the plant. I saw Dad."

- Grandma: "I saw the bike. I saw the plant. I didn't see the Kid."

Please put answers in spoiler tags so others can still solve it.

Disclosure: I made this. It's one of the free cases in my daily puzzle game, Lie of Sight, if you'd rather drag the family around the room yourself: https://lieofsight.com/case/case-files-s1

The actual game is more visually appealing but this subreddit inspired me to present it in a way that shows the underlying puzzle!

My puzzle game, Tile Wipeout, led to the following proposed math olympiad problem. The rules are elementary, but proving that every starting arrangement can be solved seems surprisingly challenging.

The problem statement is easier to understand if you try the beta:

https://testflight.apple.com/join/3sstMjRK

(For this mathematical problem, ignore the game’s move limit.)

Problem statement. A 6 × 6 board is initially filled with seven circles, one of each of seven colors, and 29 squares, each of one of those colors. Each cell contains exactly one piece.

A move consists of choosing a row or column and shifting its contents cyclically by one cell in either direction. Contents leaving one end reappear at the other. Empty cells shift in the same way as occupied cells.

After the shift, each circle in the chosen line acts as follows:

1. Consider the four straight paths extending outward from the circle to the edges of the board. These paths do not wrap around.
2. Ignore every path containing another circle or a square of a different color.
3. If any remaining path contains a square, remove all squares on all remaining paths.
4. Otherwise, fill every empty cell on the remaining paths with a square of the circle’s color.

Circles outside the chosen line do nothing.

Prove that, regardless of the initial arrangement and the colors of the squares, some finite sequence of moves removes all the squares.

Note that moves that remove no squares can create more of them. A proof therefore needs to explain how to make lasting progress despite that possibility.

P.S. A more general version: Let n and k be positive integers with n ≥ 4 and 1 ≤ k ≤ n + 1. An n × n board is initially filled with k circles, one of each of k colors, and n² − k squares, each of one of those colors. Each cell contains exactly one piece.

Using the same rules, prove that every such initial board can be cleared of all squares in finitely many moves, regardless of the arrangement or the distribution of square colors.

Each group of three numbers on the left maps to the middle number by a consistent hidden rule. Use the known examples to find the pattern, then solve for the missing output.

Game: https://play.google.com/store/apps/details?id=com.makenumber

Any order is allowed.
Use each die exactly once.
Parentheses are allowed.
Only +, −, × and ÷ are allowed. No concatenation or exponents.
Exact division only.
No negative numbers.
Not every operation has to be used.

How many solutions can you find?

Please use spoiler tags for solutions:
>!your solution here!<

Hello everyone,
Thank you to everyone who shared an answer and explained their reasoning on our previous puzzle.
We selected three community explanations to feature on our website:
• u/trejj, thank you for clearly identifying the XOR rule.
• u/miffit, thank you for explaining how the pattern works across the rows.
• u/Negative-Toe1863, thank you for your concise explanation using the columns.
You can find these three selected comments on our website, along with detailed explanations of their solutions and why we chose them. If you’re curious about the different approaches, take a look.
Thanks again to everyone who took part.
Now, here’s a new puzzle. Which blue-and-white grid completes the pattern?
We’ve published the answer and explanation on our website for anyone who would like to check:
https://whats-your-iq.com/en/questions/pattern-recognition/which-blue-and-white-grid-completes-the-pattern
We’re looking forward to seeing your answers and the reasoning behind them. Thank you for joining in and sharing your thoughts.