This is not an advert, I'm in the top 1% from around 20k users and I'm genuinely interested if it's possible to do better than the best in the world, or if they've all been mathematically shown to be the perfect answers by now. Also because it's a fun way of asking a deeper mathematics question that's almost the same.

In Tchisla you choose a starting digit (1 to 9), and a target digit (1 to 10000), and the game challenges you to use:

• your chosen digit

• + - * /

• powers

• factorial

• square roots

• brackets

• concatenation of your chosen digit

To reach your target digit, the fewer uses of your starting digit the more optimal it is. For example starting with 5 to get 30 is 5 * 5 + 5, and we can be confident that is the most optional because none of its around 20k other users have been able to do better. It shows up in a gold colour if you construct one of these best so far solutions.

The concatenation is used as so, "333 + 3 = 336, this uses 4 3's. Intermediate steps can be non-integer, for example (3/(3 + 3)) * (3 + 3) = 3. Inputting nothing is not zero, it's just invalid. Intermediate steps cannot be complex numbers. 0! = 1! = 1. You cannot take the factorial of negative and non-integer numbers. You cannot take the square root of negative numbers.

Deeper math question:

This is based on a real area of maths around these ideas, and can be made to look more like what people are actually asking in this area.

For example by using an operation set to + - * /, and one or more of:

• powers

• root(base, value)

• log(base, value)

• factorial

Or by expanding the starting number choice above 9, or limiting it to only being able to be the number "1". Or by removing limitations on intermediate values, and what operation can be done on what value type.