Tag Archives: MathsJam

Dungeons & Diagrams

This is a fun puzzle from the July 2026 MathsJams Shout.

  1. Shade squares to create walls and complete the map of the dungeon.
  2. Printed numbers indicate the number of walls in that row or column.
  3. Every unshaded square is either a hallway or part of a treasure room.
  4. Treasure rooms are always 3×3 with a single entrance and a single piece of treasure.
  5. Hallways are always one square wide. This means that, outside of treasure rooms, there will never be a 2×2 block of unshaded squares.
  6. Every dead end contains a monster. Every monster is in a dead end.
  7. All unshaded squares are connected into a single contiguous shape.
  8. Diagonally adjacent squares are never considered to be adjacent.

Example

These instructions and more puzzles (from zachtronics.com) can be found here. For example, here is a slightly more challenging puzzle.

For an interactive online version see here.

See Dungeons & Diagrams for solutions.

The King of the Spiders

Continuing the logic thread, this is a nice logic problem from MathsJam Shout for April 2025.

“The king of the spiders has four servants, and the servants have either 6, 7, or 8 legs.  Servants with 7 legs always lie, and servants with 6 or 8 legs always tell the truth.

The king asks ‘How many legs do you four have in total?’, and the four spider servants (who are standing behind a table, so you can’t see their legs) answer 25, 26, 27, and 28, respectively.

Who is telling the truth?”

Answer.

See The King of the Spiders for a solution.

Point of Intersection Problem

I came across an interesting problem in the MathsJam Shout for February 2022.

(“MathsJam is a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like.  Puzzles, games, problems, or just anything they think is cool or interesting.  Monthly MathsJam nights happen in over 70 locations around the world, on the second-to-last Tuesday of each month.  To find your nearest MathsJam, visit the website at www.mathsjam.com.”)

“Given two lines Ax + By + C = 0 and ax + by + c = 0, is there a simple link between the vectors (A, B, C), (a, b, c), and the point where the lines cross?”

The answer, of course, is yes, but the question is somewhat open-ended and I was not able to track down any answer given.

See the Point of Intersection Problem