Find it out

Source: numberthon.com

Post your answer in the comments!

If you roll 6d6 what are the odds of rolling exactly 4 unique numbers?

Every month the Momath museum in New York posts a puzzle and the YouTube channel 3blue1brown is SUPPOSED to release an accompanying video, but they've been dropping the ball pretty hard on it. This is this month's puzzle.

Im bad at probability math, but I can knock up some barely functional python code to run the simulation for me. I have the answer but It would be nice to see the actual math written out in an explain like im 5 way.

Source: numberthon.com

EDIT: 4x4 grid made up of 5*5 points/vertices

Use each die exactly once.
Any order is allowed.
Parentheses are allowed.
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, like this:

>!your solution here!<

Source: numberthon.com

No

Post your answer in the comments!

https://youtube.com/shorts/Iy26cmRvMDE?feature=share

Source: numberthon.com

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Using + and × (following standard BODMOS rules), I need to find every solution to reach the target of 11. I figure i'm missing 1 or 2, but can't find it.

Note: 1x can't be used unless necessary to connect 2 tiles

Note: 2x5+1 counts as the same solution as 1+5×2

Instead of finding words, you draw paths through a grid of numbers and operators to form equations. Each path has to match one of the target numbers shown above the board. I have added 3 difficulty levels and a clue system just in case.

my results:
Sum Adders 2026-07-19

EASY · 🟩🟩🟩🟩

⏱ 0:35

sumadders.com

Don't solve wrong answer 😭😔

Post your answer in the comments!

Source: numberthon.com

https://youtube.com/shorts/Iy26cmRvMDE?feature=share

5 GUYS GOT A RANDOM NUMBER FROM FLIPPING A COIN 0 MEANS THE PERSON IS
OUT AND 1 MEANS THE PERSON WINS BUT ONE PERSON IS A CHEATER. HOW CAN
YOU SPOT IT?

About:

As the name suggests, MiniChallenger is a scaled-down version of the math puzzle called Challenger. In most cases, a MiniChallenger puzzle can be solved within ten minutes. A set of two new puzzles is released each week. One is usually a simple problem with one or two solutions, while the other puzzle can be a bit more challenging and often has multiple solutions. Available exclusively on reddit.

Instructions:

Fill in the empty cells of the 3 x 3 grid with the numbers one to nine. It is okay to use the same number in more than one empty cell. One 'bonus' number is already placed in the center of the grid. So, the goal is to find the remaining eight digits in such a way that:

• rows in the grid add up to totals indicated on the right edge of the grid,
• columns add up to totals indicated at the top of the grid, and
• diagonals add up to totals in the upper and lower right corners.

This week's puzzles:

Solutions:

(Click on 'spoiler' boxes below to reveal solutions)

• Single-solution (left) puzzle:

[ 4 6 9 ]

[ 5 7 4 ]

[ 5 1 1 ]

• Multiple-solution (right) puzzle:

. [ 2 3 1 ] . . . . . . . [ 3 1 2 ] . . . . . . . [ 3 2 1 ]

. [ 9 5 3 ] . . . . . . . [ 9 5 3 ] . . . . . . . [ 8 5 4 ]

. [ 7 7 6 ] . . . . . . . [ 6 9 5 ] . . . . . . . [ 7 8 5 ]

. . . . . . . [ 4 1 1 ]

. . . . . . . [ 7 5 5 ]

. . . . . . . [ 7 9 4 ]

# 25+ 25+ 55+ 25+ 25+ 15+ 25= ????

Source: numberthon.com

I play this game on the train (which has a 4 digit ID) where you use + - / * ^ to make 10, every digit has to be used once no more no less factorials aren’t allowed, tetration is allowed but I can’t see it being useful, and each digit is treated as separate.
A couple examples:
5252: (5^2 - 5)/2
1234: (3*4 - 2)/1

I’ve calculated the total amount of unique 4 digit combinations to be 715, but there are some

Some obviously don’t work, 0000 being one of them.
I am wondering
A) how would you calculate them, is it a brute force solution, it is there some elegant answer?
B) what’s the answer?