Selfref #math
Expected solvable difficulty

3samples+
: experienced solvers 
keywords+
: most solvers
Level design
Tupper’s selfreferential formula is a formula that visually represents itself when graphed at a specific location in the (x, y) plane.
Tupper’s selfreferential formula, Wikipedia
\frac{1}{2} < \left\lfloor \mathrm{mod}\left(\left\lfloor \frac{y}{17} \right\rfloor 2^{17 \lfloor x \rfloor  \mathrm{mod}\left(\lfloor y\rfloor, 17\right)},2\right)\right\rfloor
This level was again inspired by a video by Numberphile a few years ago. I used to design this level as simple as possible, just throw in the image, and use the lower Y axis number as the answer. However, unfortunately, 739…944 is just too long for file names for compatibility purpose. (I literally cannot push the folder with such a long file name to GitHub.) When come to shorten an integer for checking answers, the first solution came to me was 1 000 000 007, the first 10digit prime number, commonly used in programming competitions. I finally managed to squeeze in the number in the third sample question.
Surprisingly, the first winning team reached this question before 3samples
was unlocked, way before what I was expecting when ordering the questions. Hence was confused for how such a small number was reached from the long chain of digits. I could have done better by putting the %10^9+7
hint in the actual question to make it easier.
Expected thought process
Looking at the hints,
 Find the video on the Tupper’s selfreferential formula from YouTube,
 Look for the formula in the second sample, or
 Lookup for the repository on GitHub by KellyHill that starts with T,
…to know that the question is asking about the Tupper’s selfreferential formula. Then convert the graph accordingly into numbers, and then apply \mod (10^9+7) to the answer.
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