Each sector has two outer numbers and one inner number that follow the same rule. Find the rule and work out the ?. Spoiler-tag your guess: answer 🏆 NEW: LEADERBOARD! Think you're good at this? Rule Hunter now has a daily, weekly and all-time leaderboard. Sign in, pick any nickname you like (only your nickname is shown publicly) and see if you can reach #1. Who's taking the top spot? 👉 Rule Hunter: https://play.google.com/store/apps/details?id=com.makenumber

Total weight of 5.1kg including the weight of the jar itself, wondering if anyone is able to figure it out

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/

Isn't that cool! Especially as I literally got it through pure chance

21 October is Martin Gardner's birthday, which puzzle fans celebrate as Celebration of Mind Day. Here's a wheel puzzle for it.

Trace a path through the wheel: number, operator, number, operator, … ending on a number. You can jump from any tile to any tile, but each tile can be used only once (or not used at all).

One rule to keep in mind: the path is calculated left to right, like a basic pocket calculator. So 3 → + → 6 → × → 7 evaluates as (3 + 6) × 7 = 63.

Targets to solve: 25, 34, 112, 144, 175. The video solves 25 with path 3 → × → 9 → − → 2. Find a path for each of the other four.

Bonus: every one of these numbers is connected to Gardner or to the puzzles he loved — two are about magic squares, one about Fibonacci, and two about Gardner himself. Try matching them before you peek:

- 25:  the years Gardner wrote the "Mathematical Games" column in Scientific American, 1956–1981

- 34:  the magic constant of a 4×4 magic square — every row, column and diagonal adds up to 34

- 112:  Gardner's age today: he was born on 21 October 1914

- 144:  12 × 12, and the only Fibonacci number above 1 that is a perfect square

- 175:  the magic constant of a 7×7 magic square

Please put answers in spoiler tags:  like this

For more puzzles like this, check out CalcWheel game.

Each diamond follows the same rule linking its top, left, right and bottom numbers. Find the rule and work out the ?. Spoiler-tag your guess: answer 🏆 NEW: LEADERBOARD! Think you're good at this? Rule Hunter now has a daily, weekly and all-time leaderboard. Sign in, pick any nickname you like (only your nickname is shown publicly) and see if you can reach #1. Who's taking the top spot? 👉 Rule Hunter: https://play.google.com/store/apps/details?id=com.makenumber

$$f(n) = n^3 + 54n^2 - 2917n + 20021$$ ( 40 primes)

other ones that i found

• $f(n) = n^3 + 57n^2 - 2806n + 17159$ $\rightarrow$ 39 primes
• $f(n) = n^3 + 60n^2 - 2689n + 14411$ $\rightarrow$ 38 primes
• $f(n) = n^3 + 63n^2 - 2566n + 11783$ $\rightarrow$ 37 primes
• $f(n) = n^3 + 66n^2 - 2437n + 9281$ $\rightarrow$ 36 primes
• $f(n) = n^3 + 69n^2 - 2302n + 6911$ $\rightarrow$ 35 primes
• $f(n) = n^3 + 72n^2 - 2161n + 4679$ $\rightarrow$ 34 primes
• $f(n) = n^3 + 120n^2 - 2893n + 2131$ $\rightarrow$ 33 primes
• $f(n) = n^3 + 75n^2 - 2014n + 2591$ $\rightarrow$ 33 primes
• $f(n) = n^3 + 4n^2 - 1081n + 12289$ $\rightarrow$ 33 primes
• $f(n) = n^3 + 78n^2 - 1861n + 653$ $\rightarrow$ 32 primes
• $f(n) = n^3 + 7n^2 - 1070n + 11213$ $\rightarrow$ 32 primes
• $f(n) = n^3 + 125n^2 - 4412n + 27823$ $\rightarrow$ 31 primes
• $f(n) = n^3 + 54n^2 - 2329n + 20507$ $\rightarrow$ 31 primes
• $f(n) = n^3 + 10n^2 - 1053n + 10151$ $\rightarrow$ 31 primes
• $f(n) = n^3 - 20n^2 - 561n + 10223$ $\rightarrow$ 31 primes
• $f(n) = n^3 - 25n^2 - 292n + 4877$ $\rightarrow$ 31 primes
• $f(n) = n^3 + 128n^2 - 4159n + 23537$ $\rightarrow$ 30 primes
• $f(n) = n^3 + 101n^2 - 3080n + 13537$ $\rightarrow$ 30 primes
• $f(n) = n^3 + 71n^2 - 2690n + 14197$ $\rightarrow$ 30 primes
• $f(n) = n^3 + 57n^2 - 2218n + 18233$ $\rightarrow$ 30 primes
• $f(n) = n^3 + 20n^2 - 2099n + 23581$ $\rightarrow$ 30 primes
• $f(n) = n^3 + 23n^2 - 1988n + 24223$ $\rightarrow$ 30 primes
• $f(n) = n^3 + 45n^2 - 1936n + 7307$ $\rightarrow$ 30 primes
• $f(n) = n^3 + 13n^2 - 1030n + 9109$ $\rightarrow$ 30 primes
• $f(n) = n^3 - 17n^2 - 598n + 9643$ $\rightarrow$ 30 primes
• $f(n) = n^3 - 22n^2 - 339n + 4561$ $\rightarrow$ 30 primes
• $f(n) = n^3 - 28n^2 - 119n + 4219$ $\rightarrow$ 30 primes
• $f(n) = n^3 - 37n^2 + 162n + 3517$ $\rightarrow$ 30 primes
• $f(n) = n^3 - 62n^2 + 781n + 227$ $\rightarrow$ 30 primes
• $f(n) = n^3 - 188n^2 + 2161n + 443$ $\rightarrow$ 30 primes

Hey everyone! We created a daily math grid game called QuizSum where you use arithmetic tiles to reach a daily target number. Speed Mode gives you 3 hidden paths to find against the clock, while Pro Mode offers dozens of unique solutions.

Today's Speed Target is 250. Give it a spin and let me know your fastest time!

🔗 
www.quizsum.com

Hey everyone! We created a daily math grid game called QuizSum where you use arithmetic tiles to reach a daily target number. Speed Mode gives you 3 hidden paths to find against the clock, while Pro Mode offers dozens of unique solutions.

Today's Speed Target is 250. Give it a spin and let me know your fastest time!

🔗 
www.quizsum.com

Each pair of numbers produces the number below it by the same hidden rule. Solve for the missing number from the pattern shown by the other pairs. 🏆 NEW: LEADERBOARD! Think you're good at this? Rule Hunter now has a daily, weekly and all-time leaderboard. Sign in, pick any nickname you like (only your nickname is shown publicly) and see if you can reach #1. Who's taking the top spot? 👉 Rule Hunter: https://play.google.com/store/apps/details?id=com.makenumber

シグマの公式から秒でわかるけどなんかめっちゃ美しくね？