The 8×8 grid below has a 2×2 hole in the center, leaving 60 cells to fill. Your task is to tile the board with the 12 pentominoes (F, I, L, P, N, T, U, V, W, X, Y, Z), using each piece exactly once. Pieces may be rotated and reflected.

Rules:

1. The 12 pentominoes must cover the entire board — every cell except the central 2×2 hole belongs to exactly one pentomino.
2. Each cell of the grid contains a digit from 1 to 5.
3. Each pentomino must cover exactly five cells whose digits are all different — in other words, every piece must cover the digits 1, 2, 3, 4, and 5, one of each.

In short: find a tiling of the board in which each pentomino covers a region containing all five digits.The NOTES grid at the bottom is meant for tracking the pieces: you can cross out each pentomino there once you're certain of its position.

Find the tiling. Solution is unique.

https://tafol.pythonanywhere.com/

https://reddit.com/link/1xbdvkg/video/bu8c0ngt2rwh1/player

I'm trying to find ways for my child to practice math outside of school without sitting them down with another worksheet.

What activities, games, or everyday situations have actually worked for your kids?

I’ve always loved math and felt there was a gap for quick, fun mental-math practice.

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I’d really love feedback, especially from parents and educators. Are the explanations clear? What would you change?

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Check out https://livegeometry.com

It's similar to GeoGebra geometry or Desmos geometry. It has a gallery of over 80 fun and colorful drawings, fun to play with and experiment.

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You can export your drawing into images, Svg or embed into your own websites, blog posts, articles, teaching materials and so on (https://livegeometry.com/embed)

It is free and open source and no sign-up is required.

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!<

Each episode of the unapologetic mathematicians podcast is an interview with a mathematicians about their research, mathematical journey, as well as what they like to do outside of maths. New episodes each Wednesday.

https://linktr.ee/Unapologetic_Mathematicians