spiromania #76
for Pi-day 2024
This is a puzzle cache.
The cache is not at the posted coordinates.
Rather, it's at
N44 21.ABC W92 56.DEF
where A to F can be determined
from the six questions below.
Consider building a diagram, such as the one above, based on the digits in Pi, viz. 3.14159..., in base 10. Beginning at the dot in the middle on the left, we'd first go 3 units north, then 1 unit east, 4 units south, 1 unit west, 5 north, and so on. The diagram is through the first 32 digits in Pi. Why stop there? Because a decision has to be made since the next digit is 0. What to do? The rule generally used is to still make the right turn but stay in place but turn right again. This results in a U-turn, or about-face.
The big question is would we ever return to the starting point? The answer is I don't know, and I don't think anyone else does either. I've tried it through one million places without success. But that doesn't mean it won't happen.
If at first you don't succeed, try something simpler. Okay. Rather than starting at 3, let's start farther on down the line, beginning at the 1 then the 4, etc. and see if we ever return to the starting point. Finally, beginning at the 139 place, we get a sequence of 29 digits that produces an early return. That's shown below. I've deemed it the world's first "pilateral".
The first few digits in that winning sequence are 17253. Check it out beginning at the big dot. North 1 unit, east 7 units, etc. Eventually it returns to the starting point. Here then are the questions:
A Which digit A occurs A times in the sequence?
B What is the penultimate digit?
C How many 6s are there?
D What digit occurs three times in a row?
E What is the last digit?
F How many times does the digit 0 occur?
Before entering your solution N44° 21.ABC' W92° 56.DEF' into the coordinate checker,
see that the sum of A through F is 17.
You can validate your puzzle solution with
certitude.
More than you need to know: The lateral spiral above ends going north. The next turn would be to the east. Repeating the sequence three more times results in the pilateral tiling below.
Congrats to the first 10 solvers:
1. Huitzlipochtli Fri, 15 Mar 2024, 04:57:05
2. Jittney Fri, 15 Mar 2024, 05:55:17
3. MNBorris Fri, 15 Mar 2024, 06:12:11
4. toolrep1 Fri, 15 Mar 2024, 06:30:35
5. NYWanderer Fri, 15 Mar 2024, 08:26:10
6. salsman Fri, 15 Mar 2024, 08:40:28
7. sparkyfry Fri, 15 Mar 2024, 11:23:29
8. mnboyscout Fri, 15 Mar 2024, 12:18:26
9. foundinthewild Sat, 16 Mar 2024, 01:20:03
10. kkmk Sat, 16 Mar 2024, 16:31:38