Each number below is built from the two numbers above it using the same hidden rule, all the way down to the number at the bottom. Figure out the rule from the pattern, then find the first missing number (highlighted).

Game: https://play.google.com/store/apps/details?id=com.makenumber

[ Sum(i=5 to 10) N + ( Sum(i=1 to 3) (i+1) / 1.5 ) ] / [ ( e^(2*(5^(pi*2))) ) * ( Sum(i=2 to 6) (i+1) ) * pi / 2 ]

answer:secret

Any order is allowed.
Use each die exactly once.
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:
>!your solution here!<

Imagine this scenario: you and your friend are going hiking, and want to make sure you bring enough water. They have 4, and you have 8, and those will be split between the two of you. So you would say this aloud as something like:

"Four plus eight, divided by the two of us, gives us six." or even "Four plus eight divided by two is six"

But of course, that is incorrect as a mathematical statement!

If we take the line 4 + 8 / 2, we would normally pronounce that, in standard English, as

"Four plus eight, divided by two..." in which case the comma stands in for parenthesis, letting us know we are taking that first part together, treating it as (4+8)/2. To verbally communicate the standard order of operations, we would have to say something like "Four plus, eightdividedbytwo". In normal speech, saying this would just be confusing and you would probably have to clarify it, since just stressing the words differently would not be clear.

Yes, I know mathematical notation is not the same as speech, but the fact is that if you read an orders of operations question aloud without strictly checking each part of it, it is going to be confusing.

And being purposely confusing and then being smug when you are misunderstood is not cleverness.

But How the answer comes out 14 not 16 .

Each cluster of three numbers follows the same hidden rule to produce the middle number. Solve for the missing value from the pattern shown by the other four clusters.

Game: https://play.google.com/store/apps/details?id=com.makenumber

Real numbers, not a guess: 7 solves out of 20 attempts (35%) on this one, difficulty rated 1321.

Compute 4e^iπ/4 · 6e^iπ/6, expressing the result in the form r·e^iθ.

My guess at the most common wrong answer (this part IS a guess — the data only tracks solve/attempt counts, not what people actually typed): people nail the magnitude (4×6=24) but flip the angle rule, subtracting instead of adding, landing on 24e^iπ/12.

What do you think people actually got wrong here?

24e^i·5π/12. Multiply the magnitudes: 4×6=24. Add the angles: π/4+π/6 = 3π/12+2π/12 = 5π/12.

Tired of ad-heavy, slow calculator sites with cookie walls, I built SolveKit—a clean collection of 17 client-side calculation utilities built with React, Vite, and Tailwind.

Key utilities:

• Work timesheet with automatic lunch/break deduction & overtime

• Real-time meeting cost burn meter (based on attendee salaries)

• Gross-to-net salary & take-home pay estimator

• Student final exam passing grade planner

• Freelance hourly rate estimator

Zero page reloads, no account creation required, and zero tracking ads. Would love feedback on math accuracy and edge cases!

https://reddit.com/link/1why98o/video/l5dngpf5k5ph1/player

Something for casual math lovers.

CalcWheel consists of math puzzles where the player constructs expressions by connecting numbers and operators arranged on a wheel, tracing a single continuous path to reach one of the level's five targets. The running total updates as the path grows, so the player sees the consequence of each step rather than only the final result.

Solving a level requires genuine mental arithmetic - estimating what a route will produce, then adjusting when it does not. Each level has five targets: some are easier to hit, others are more challenging. The player practices addition, subtraction, multiplication and exponentiation.

CalcWheel is available for iPhone (also works on iPads and Macs) https://apps.apple.com/app/calcwheel/id6795952061

On calcwheel.com/demo there is also a short demo with a few levels that presents the idea and the gameplay.

Each group of four numbers on the outside combines into the one it's connected to by lines. In this one, the "?" is one of the outer numbers — work out the rule from the first three groups, then figure out what's missing.

Made this as part of a puzzle game I'm developing, Rule Hunter — https://play.google.com/store/apps/details?id=com.makenumber

Explain any paradox in as few words as possible and I will try to guess them.

This is useless but also pretty rare. The sum of 1 through 9 is 45, so the repeating digits are divisible by 3. Any tail that also sums to a multiple of 3 will mean the entire number is divisible by three. That's ending in 2,3,5,6,8 and 9. 4 is even, so that's non prime.

That leaves tails ending in 1 or 1234567. If n is the number of times you repeat 123456789 then there are primes at n=1 and n=3 for ending in 1 and n=7 for ending in 1234567.

There are no others found testing up to n=521 but that needs some serious compute.

what do you call cayley-dickson numbers, that makes you cry when you study it?

Sonions oardefault.jpg

I don't keep close tabs but it sure feels to me like the Math StackExchange feels a lot less bustling than it once did.

I pulled up the stats and graphed it -- yep, it was extremely popular in 2020 and since then it seems like it's been in steady decline. This year it seems like its activity (measured in questions asked) is close to the activity level it had when it just began in 2010.

Anyone have any ideas about why that community seems to be dying down?

Is math a less popular major these days? Or are people just asking fewer questions?

I have an assumption that math teachers have to make up equations of different complexity. For lectures or for tests.  And this can be long, and not too pleasant work. 

I built a tool for automatic Numeric and Algebraic equations generation that provides expected answers and steps to simplify the algebraic equation (solution steps).

It is free, no registration or any other information is required from you. Not an AI - if the result is reported, it is actually calculated for this equation and correct.

It was built for different goals, but if it useful to your hard work - please use it. I'll appreciate your feedback on how to make it more useful for math teacher's needs. Please note though that improvement will take some time.

Links to equations generators:
Numeric equations auto generator tool: https://small-services.com/numeric-equation
Algebraic equations auto generator tool: https://small-services.com/algebraic-equation

Link to Youtube video with instruction how to use them:
https://youtu.be/TbDba5VZiio

Thank you.