Another Thursday means that it is time once again for NVIDIA’s #Orderof10 Origins challenge. Just as a recap, each week NVIDIA is giving away two GTX 1080 graphics cards and a ton more to lucky participants who get selected in a random drawing. How do you gain entries? Simple. Answer a weekly puzzle via http://www.orderof10.com, the actual answers themselves, are not particularly simple to arrive at hence, here at Modders-Inc.com, I write a puzzle guide for those who are curious about solving it. I am not joining the giveaway myself and am only doing this to help others but if you want to pass along some goodwill (some positive karma if you will), simply use a referrer code left by some of our commenters in the previous weekly challenge articles when you sign up.
Link to previous answer guides:
Now on to this week’s puzzle. The #Orderof10 Origins website shows the following image:
The text reads: “John Lloyd Stephenson was perhaps the most intrepid explorer among our order, inspiring countless archaelogical expeditions to Yucatán and its ancient Maya cities. World-builders in every sense of the term, the Maya were advanced mathematicians who weaved their deep understanding of the universe into every aspect of their culture, including their architecture.”
Google says John Lloyd Stephenson is an actor from England so NVIDIA probably meant John Lloyd Stephens who was a an American explorer whose focus was on Mesoamerican cultural studies. As usual however, the named scientist is not actually useful to solving the puzzle at all just like all the named scientists in the first two weeks were not necessary.
What is vital to solving this week’s puzzle however is very apparent from the rest of the clues in the image. At the top is the Temple of Kukulkán, an easy recognizable sight from Chichin Itza. Although it is not a large pyramid, it is nonetheless interesting because every spring and autumn equinox, the sun casts a shadow to the side creating an image of a plumed serpent crawling down the side. The Mayans were particularly fond of serpents as well as math and astronomy. Just like it is described in the puzzle clue, these are incorporated in every aspect of their culture.
Right below the photo of the pyramid temple is a wheel coder showing the Mayan number system and matching glyphs. Unlike our decimal number system, the Mayans used a vigesimal or base 20 number system. We use 0 to 9 as fundamental numbers to form the rest while they use 0 to 19. The sticks, stones and shells strewn about the page are the original inspiration for the Mayan numerals. Pebbles from one to four denote the first four values in increasing order, five to nine are denoted with a stick in combination with one to four pebbles, 10 to 14 uses the same symbol except with an additional stick and 15 to 19 uses the same idea except with three sticks. The shell denotes a zero value, and in fact this made the Mayan number system ahead of everyone else during their time period. The earliest in recorded history outside of Mesoamerica did not show up in India until the 5th century. The concept of zero is believed to have been invented by the Olmecs and the earliest evidence dates back to 32BCE.
Below the glyph wheel is the actual puzzle, which oddly enough resembles the Temple of Kukulkán from the top view. It also has nine levels with an access staircase running down the middle of each side of the pyramid. Using the wheel coder and judging by the puzzle sheet, it looks like a pretty straightforward conversion so let us begin with that.
Next, we plug in the converted numbers to the puzzle sheet with the matching skull-based glyph:
Now we have an interesting puzzle here because there does not seem to be a pattern to the way the glyphs are positioned. The south-west quadrant is the only one that looks like it has some pattern, so we are going not going to factor the number placement in the solution. Plus we have too many numbers here on our hand and we need to figure out how to condense it into one. Another clue is the plus and minus sign on the corner of each quadrant. So far, we have many of the characteristics of the previous week’s puzzle on our hand except for one: the tedious grind that the puzzle-master seems to demand every week. It has been very simple so far so looks like we actually have to do some math here.
There are nine steps and nine numbers per quadrant to deal with. Remember that the Mayan’s incorporate the plumed serpent, architecture, math and astronomy in everything they do as the text clue says so that is what we need to think like. There are nine numbers per quadrant and there are nine platforms on the pyramid. The serpent on this pyramid climbs down from the top (from the heavens). This probably suggests that the order of the numbers begins at the top or when transposed on the image of the pyramid temple, at the center:
- NW = 14 15 01 05 01 19 01 04 15
- NE = NN NN 06 14 11 13 19 01 12
- SE = 01 16 17 15 00 19 05 10 13
- SW = 10 14 14 16 04 10 10 18 16
Also, remember that the Mayans use base 20 instead of base 10. We have nine numbers per quadrant exactly and when we don’t, we have a null value. In our decimal number system for example, 12493 can be written as:
- 1 * (10^4) + 2 * (10^3) + 4 * (10^2) + 9 * (10^1) + 3 * (10^0)
With a vigesimal number system, the base is 20 not 10 but the same idea applies. Let us try that with our numbers on hand but let us do it as the Mayans do and write it from top to bottom then add the resulting value starting with the North West quadrant:
- 14(20^8) = 358400000000
- 15(20^7) = 19200000000
- 01(20^6) = 64000000
- 05(20^5) = 16000000
- 01(20^4) = 160000
- 19(20^3) = 152000
- 01(20^2) = 400
- 04(20^1) = 80
- 15(20^0) = 15
- NW = 377,680,312,495
This is the long form and of course you can do it directly like the layout with the base 10 example so you can feed it easier into something like Google which will crunch out the result for you. Now let us continue on with the other four quadrants since there is still the plus and minus sign on each corner to deal with after.
- NN(20^8) = 0
- NN(20^7) = 0
- 06(20^6) = 384000000
- 14(20^5) = 44800000
- 11(20^4) = 1760000
- 13(20^3) = 104000
- 19(20^2) = 7600
- 01(20^1) = 20
- 12(20^0) = 12
- NE = 430,671,632
- 01(20^8) = 25600000000
- 16(20^7) = 20480000000
- 17(20^6) = 1088000000
- 15(20^5) = 48000000
- 00(20^4) = 0
- 19(20^3) = 152000
- 05(20^2) = 2000
- 10(20^1) = 200
- 13(20^0) = 13
- SE = 47,216,154,213
- 10(20^8) = 256000000000
- 14(20^7) = 17920000000
- 14(20^6) = 896000000
- 16(20^5) = 51200000
- 04(20^4) = 640000
- 10(20^3) = 80000
- 10(20^2) = 4000
- 18(20^1) = 360
- 16(20^0) = 16
- SW = 274,867,924,376
Ok, now we are down to four numbers and we apply the minus and plus sign per quadrant and crunch into a single number:
+377,680,312,495 – 430,671,632 +47,216,154,213 -274,867,924,376 =149,597,870,700
Now we are back to a nine digit number which just happens to be the official agreed upon, astronomer approved distance of the sun from Earth!
Good luck and see you next week for the final #Orderof10 Origins challenge. Feel free to leave a comment or suggestion below.