ABC=321

CDE=543

AEF=651

FAC=??

Can You Solve It ? Comment Your Logic!

Only the top ball moves. It can go into any tube with free space (max 5 balls), whatever the color, and there are no empty tubes to use as a buffer. Target: every tube ends up exactly like the goal, bottom to top blue, orange, pink. Minimum is 10 moves. Please put your solution in spoiler tags (moves written like 3→2). Puzzle is from my game Ball Sort Pattern.

if we have a 4x4 grid of squares in which we can place letters of the English alphabet, one in each square then find the maximum number of possible 4 letter words formed if repeating letters is allowed. for example.

A F A T

B E S H

M R X E

G D F E

rule to follow: if you choose a letter tile for the starting letter of your word you must choose the tile adjacent to it ( diagonals count) for the second letter of your word and continue until u get a 4 letter word. for example, in the example above if you choose F as the first starting letter u must select any 5 of the tiles surrounding it as the next letter of your 4 letter word. by choosing F then A then T and then S , you get FATS so like this you must form 4 letter words and have to find the maximum number of 4 letter words possible if repeating letters is allowed( as shown, A is repeated in example and so is E)

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!<

I couldn't solve it. AI says that puzzle has 1 solution. But i couldn't find it

Each fruit symbol stands for a fixed number. Use the solved equations to work out what each symbol hides, then find the missing sum. (Puzzle from the game Rule Hunter)

Hey math puzzle fans! Here are today’s two daily QuizSum arithmetic challenges:

⚡ SPEED CHALLENGE
🎯 Target Number: 75
🔢 Available Digits: 5, 10, 15, 20, 25
➕ Operators Allowed: +, -, ×, ÷
Goal: Find 3 distinct equation paths that reach 75!

🧠 PRO CHALLENGE
🎯 Target Number: 80
🔢 Available Digits: ,5, 8, 12, 16, 20
➕ Operators Allowed: +, -, ×, ÷, (, )
Goal: How many total valid equation paths can you discover?

Drop your solutions in the comments below using spoiler tags like this: (25 - 2) * 6 - 4

How many unique paths can you find for each?

Each pair of numbers produces the number below it by the same hidden rule. Work out the rule from the known pairs and find the missing number. (Puzzle from the game Rule Hunter)

Each number on the left is turned into the number on the right by the same hidden rule. Work out the rule from the known examples and find the missing output. (Puzzle from the game Rule Hunter)

Think out of the box, and post your answer in the comments!