In celebration of Anti-Pi Day (September 14, as far from Pi Day as you can get), I present the following. I recently wondered "Do any places in pi reference themselves when taken as indices?" That is to say, are the digits at the ABCth place of pi ABC? The first one of these is trivial: the first place in pi is 1 and so it points at itself. The next reflexive pi place is the 16470th place, where we find the digits 16470.
That's all well and good (and there will probably be a puzzle on that in the future) but then I wondered if there were pairs of indices that pointed at each other. That is to say, if the digits at the ABCth place of pi are XYZ, are the digits at the XYZth place of pi ABC? The first such pair shows up quickly, at 79 and 99. Again, more fodder for a future puzzle.
I then went a bit crazy, and started searching for longer chains that completed circles within pi. That is to say, the digits ABC of the first index point to DEF at the second, which point to GHI at the third, etc., until eventually some digits (let's call them XYZ) point back to the starting location. Your goal is to find the first *25 node* circle in pi, such that the digits at the 25th node point back to the first location. For sanity's sake, all of the nodes will have the same number of digits, which may or may not match the examples already given.
Once you have found this circle within pi, use it to key two cipher key squares. The first square you should key by sorting the nodes from lowest to highest, then assign the letters A-Z (skipping J) starting with A for the lowest value, then return the nodes to their original circle order with the lowest value first. For the second square, assign the letters A-Z (skipping J) to nodes following the circle (once again starting with the lowest value). Then sort the nodes from lowest to highest and make a key from the letters in that order. CONSULT THE TWO DIAGRAMS LINKED BELOW FOR CLARITY IN UNDERSTANDING THESE KEYING METHODS
Now use the two squares to solve the following cipher:
VU SA EE TN ON FW RE FD RI MG EZ NE KN EZ QF KF ZP RI LC AE MV UE BA CB WG GF DD LK QQ XL NX MG OC UO QF KF GP RE LX XP HO QW WG TP EA TR RE ED UR DS EW GP TN SC ON WG PV ES VP NX CD QW HF TY RE SM GP HM GL TO BX NB KK QF TS RE SM GP
Simple, right? Good luck!
Congrats to ddlatham for FTS and FTF!
You can validate your puzzle solution with certitude.