Can you solve this AI/Math puzzle and get a prize? I couldn’t.

I found a poster with a math puzzle that points to a reward website. I couldn’t figure it out, so maybe the prize is still available!

Here it is all typed out:

prefix(
    [
        3!
        + argmax(
            softmax(
                [log(2), pi + e]
            )
        )
        + log*(16)
    ] ^ [
        BusyBeaver(4)
        + ⌈H100 flops / A100 flops⌉
        + 1
    ]
)

.ai/givemeprize

Stop here if you want to work on the puzzle yourself!

My Breakdown

Below is everything I figured out before I got stuck.

• argmax refers to numpy.argmax returns the index of the maximum in an array
• softmax is more interesting. Wikipedia’s definition is complicated, but pytorch explains it concisely around normalizing probabilities to sum to 1.
• log is maybe log₂ because of the computer context, maybe log₁₀, but probably log_e because numpy and pytorch both assume log_e.
• log* is confusing. I’ve never seen that syntax before. Is that natural log, aka log_e? I’m guessing it’s log₂ because the argument is 16, which makes a nice and round answer of 4, like the rest of the problem.
• BusyBeaver(4) is either the maximum shift 107 (likely) or the maximum score 13 (original)???
• H100 flops and A100 flops are the flops on the H100/A100 Nvidia chip. There are so many variations. But “H100 flops/A100 flops” is surrounded by upper brackets, which is ceil. Thus, I only need a best guess. Running through a few numbers, I get around 3.04 to 3.5, so ceil is 4.
• prefix is weird, but I’m guessing it’s the integer portion of the number, not the decimal portion.

Here’s my reduced form:

prefix(
    [
        6
        + argmax(
            softmax(
                [0.693147181 , 5.85987448]
            )
        )
        + 4
    ] ^ [
        107
        + 4
        + 1
    ]
)

.ai/givemeprize

I don’t need to run softmax, because I know the second number will be bigger and argmax will return its index. Argmax is zero-based, so that reduces to one.

prefix(
    [6 + 1 + 4] ^ [107 + 4 + 1]
)

.ai/givemeprize

Again, reducing by simple math:

prefix(
    [11] ^ [112]
)

.ai/givemeprize

Maybe the answer was 11.ai/givemeprize, but now it 404’s. They’re not based in SF, so I doubt it.

Open questions:

• What is a prefix function that takes only one number?
• Should BusyBeaver(4) be 107 or 13? 107 is very large for an exponent, but it’s technically possible. 11 ^ 112 is 112 digits long, and the maximum domain name length is 253 characters long.
• What is log*? I could try log₂ or log₁₀. log_e is also possible, but I’ve only seen it written as ln.

That leaves these options:

	BusyBeaver(4) = 13	BusyBeaver(4) = 107
log2	prefix(11 ^ 18) = 5559917313492231481.ai/givemeprize	prefix(11 ^ 112) = https://4.3249464815*10^116.ai/givemeprize
log10	prefix( (7 + log10(16)) ^ 18 ) = 28351501028247453.ai/givemeprize	prefix( (7 + log10(16)) ^ 112 )
loge or ln	prefix( (7 + ln(16)) ^ 18 ) = 93742854.ai/givemeprize	prefix( (7 + ln(16)) ^ 112 )

I considered looking at recently registered domain names. I could filter by domains only containing numbers and under the *.ai TLD. I could hit them all at /givemeprize and see who responds at all and without 404. Unfortunately, that information is behind paywalls.

I love puzzles, but I’m done with this one. I don’t think I get it. Maybe I missed something.

The Last Bits

Someone left the correct answer in the comments, but didn’t show any of the work, which is frustrating cause I want to understand!

However, folks at lobste.rs guided very kindly and I figured out my mistakes!

• log* is iterated log. I could have learned this if I used ChatGPT or WolframAlpha instead of Google.
• BusyBeaver(4) is 13, my less likely answer
• this makes the exponential 10^18
• prefix in the context of 10^18 is the SI prefix, like EXAbyte or TERAflops. So the answer here is exa.

I somehow got a lot more traction on HackerNews way after I posted.