u/Gurbuzselimboyraz

Hello everyone! I believe this will get a lot of downwotes because there has been a challenge recently (the 6 fours challenge) from another user, and this might seem as an attempt to copy it. This is not a copy.

My friend dared me to go from 2 up to 100 using 1 2 3 and 4 only once. The allowed operators are +, -, and exponents. No multiplication, and no parenthesis. I filede at 7. Can someone find a way to do this, or is it impossible?

Edit: There has been some confusion about being able to smush digits. You can do 1³24 to get 24. Also, the multiplication symbol is not allowed, but expressions like 2³1⁴ are allowed.

Edit 2: The number 30 does not seem possible. I have not been able to find it using gemini and chatgpt. Can you guys verify it? If so, which numbers are impossible?

Edit 3: HUGE NEWS!! ³2+14 = 30 is allowed. I told my friend the problem with the number 30. After a while of begging, he let me use tetration! Huge thanks to Bonk_Boom for the solution:)

Edit 4: There is some confusion about concatenation, it is allowed.

I don't know where to post this...

The photo here shows my attempt on continuing x^x to negatives. My reason to do this is not because I want to, but that desmos is very bad at calculating x^x where it can be calculated, amd it forces me to. Even when i took an absolute value for the imag.vals, it still couldnt compute. The approach that i took was taking closer and closer limits to the function. That went horribly. After increasing the slider to simulate the limit, the graph had x coordinates where it would be cut. Its because of rendering, bcz when i zoom in, the cuts are smaller.

Then, i wanted to do this:

X^x=e^ln(x^x)

=e^xln(x)

=e^x×e^lnx

=xe^x

But when i graph this, the result is absurd.

What can i do, and why does this happen?

Link: https://www.desmos.com/calculator/fuoihysdfd

https://www.desmos.com/calculator/fuoihysdfd