# Peg the Panel to Procure the Prize

## I AM AN IDIOT AND HAD THE WRONG NAME FOR THE NEMESIS

I'm a little worried now that the pattern won't get recognized because it's requires an "Aha!" leap that is only obvious to me because I designed the puzzle. I'll try to give a few more helpful hints and see what happens.

Before he was an evil overlord ruling with an iron talon over a realm of darkness, Hooty McOwlface was Harold McArthur and was a world-renowned adventurer. He sought treasure and fame. On one particular undertaking, he came across what appeared to be an ancient tomb buried deep within the Amazon. After defeating the usual gambit of traps and tricks, he came upon a gilded room. His torch created stars on the polished walls and all the world was gold. Aside from the plating, though, there was no treasure.

Although he was at first frustrated by what he took to be the evidence of grave robbers, his hope renewed upon spying a single silver brick on the opposite wall. When his fingers brushed against it, he was surprised to find it was warm and moved under his touch. With a smooth motion, it slid up and under the tile above, revealing a panel lit from within. There was a 9x30 grid of holes, many of which had small pegs inserted into them. It reminded Harold of a toy from his childhood that let you create lighted artwork with small, plastic pegs.

There were five pegs laying on a tray just underneath the panel. They each had a faint glow and some kind of marking on the side but, aside from that, they looked exactly like the pegs already inserted into the panel. Experimentally, he stuck all five into random open holes. Nothing happened. He tried to pull out one of the pegs that were inserted to begin with but it was stuck fast. He couldn't just try every possible combination because there were almost 572 million possibilities and Harold had forgotten to pack lunch.

After studying the panel for a while, a glimmer of recognition formed. He picked up a peg and stuck it into a particular open hole. Nothing happened but he was confident so he went ahead with the rest. Once all five were in, their glow vanished! The panel slid shut and a vibration started under his feet. Slowly, ever so slowly, the entire wall to the right of the panel slid aside.

As Harold raised his torch and peered inside, a loud bang nearly gave him a heart attack. Suddenly, his face was peppered with something small and slick. When he recovered from the shock, he saw that he had been shot with a confetti cannon. The colored paper littered the floor. Looking up, he saw the only thing in the secret room: a banner that read "GOOD JOB!"

Angered at the waste of his time, he stripped every ounce of gold from the walls and used it to hire his first henchmen and take his vengeance upon the world.

Would you have been able to solve the panel in time for lunch?

In the image below, The white squares with a hollow circle represent empty holes. The black squares with the double white circle represent holes with pegs in them.

These are the pegs exactly as they appeared to Harold. They should be used to fill in five of the empty holes in the image above.

To alleviate any chance of confusion on the characters, here is the text from each peg:

Blue Peg (ϠϕϞζ)
--------------------
Ϡ   03E0   Sampi (Archaic)
ϕ   03D5   Phi (Symbol)
Ϟ   03DE   Koppa (Capital)
ζ   03B6   Zeta (Capital)

Red Peg (ΫΘβγ)
--------------------
Ϋ   03AB   Upsilon (Capital with Dialytika)
Θ   0398   Theta (Capital)
β   03B2   Beta (Lowercase)
γ   03B3   Gamma (Lowercase)

Green Peg (θγΘϞ)
--------------------
θ   03B8   Theta (Lowercase)
γ   03B3   Gamma (Lowercase)
Θ   0398   Theta (Capital)
Ϟ   03DE   Koppa (Capital)

Purple Peg (φβΣθ)
--------------------
φ   03C6   Phi (Lowercase)
β   03B2   Beta (Lowercase)
Σ   03A3   Sigma (Capital)
θ   03B8   Theta (Lowercase)

Orange Peg (ΔΣβΨ)
--------------------
Δ   0394   Delta (Capital)
Σ   03A3   Sigma (Capital)
β   03B2   Beta (Lowercase)
Ψ   03A8   Psi (Capital)


One of Harold's first henchmen was heard to be retelling this story in a tavern shortly after receiving his first paycheck. It turns out that Harold was pretty upset about how he had been tricked and was telling everyone. As it turns out,

the peg colors were a red herring.

The first thing Harold did after hiring his first henchmen was to hunt down whoever created that temple. After all, based on the solution,

he knew it was a recent creation and not an ancient one.

As it turns out, the perpetrator was none other his old nemesis:

Lord Augustus.

Of course, that's just what Harold's nemesis called himself once he rose to power. To annoy his, Harold called him by his original name:

August

What infuriated Harold the most is how he was tricked into thinking it was an ancient temple. Once he recognized the pattern, he knew it couldn't possibly have been older than

the 1870s because the pattern it references wasn't invented until that decade.

What was even more infuriating was all the distracting extra information. Someone was just trying to make explorers waste time.

The characters inscribed on the pegs were also a red herring! In reality, it didn't matter which peg went where! The only thing that mattered was which five holes got filled in.

If you asked Harold how he managed to find the pattern behind the pegs, he would explain that he tried breaking it up into pieces for analysis. What worked the best was when he

divided the first three rows into 3x3 blocks.

Knowing what his made his nemesis famous, the grid started to make sense.

• If Harold only had to get one peg correct at a time (rather than all five at the same time), wouldn't it be reasonable to try all holes with each peg? Oct 23, 2015 at 19:22
• @dpwilson I got carried away with the flavor text and forgot myself. I've fixed it now. Thanks. Oct 23, 2015 at 19:26
• Cool, thanks! Time to get cracking. Oct 23, 2015 at 19:27
• Is the last letter on the fifth (yellow) peg a capital or lowercase psi? Oct 24, 2015 at 3:28
• @2012rcampion I think it's capital, because it doesn't extend as low as the beta next to it.
– f''
Oct 24, 2015 at 3:29

Harry thinks his nemesis is August Dvorak (1894–1975), but is mistaken.

Based on Toast's comment:

Also, only the first row of your grid is correct. The next two are... off.

I prepared an alternate dissection of the grid:

Of course, anyone who knows a Dvorak user knows that they avoid QWERTY like the plague. The puzzlemaker is more likely a descendant of Christopher Latham Sholes (1819–1890).

After f'' showed me how to tie strings between the pegs in order to form letters, the solution was easy:

The new peg positions are highlighted in red.

• Oh, crud! I tried to get fancy with my naming and my little formula crapped out on the Capital / Lowercase naming. I also misunderstood the "Phi Symbol" as being archaic, probably because it's right before the archaic symbols in my character map and there was already a capital and lowercase version of phi. Thanks for the correction on those. I'll fix the hint. Oct 26, 2015 at 17:59
• @EngineerToast The Unicode consortium has a list of the official names (although I find it easiest to use CharacterName). Oct 26, 2015 at 18:03
• I think U+03D5 GREEK PHI SYMBOL is meant for when you want to guarantee that you aren't getting the "curly" phi. Oct 26, 2015 at 18:05
• It might be marking just the angles and endpoints of the letters, not the whole shape.
– f''
Nov 18, 2015 at 23:13
• OMFG. bangs head on desk On the plus side, I now know about Baudot code, Braille, several 19th century guys named Antonin, a couple of British diplomats, and Greek numerals. Learning is power! Nov 19, 2015 at 13:58

This is a long shot, but...

...on the Wikipedia page, we find 31 different symbols in the (old) Greek alphabet. Since there are exactly 30 columns, it leads me to think there is a mapping between the symbol and the column, presumably $[0,30]$. Now, there are four of the symbols and there are also colours, so we have way more information than is needed to get a position in the peg matrix. However, if the colour of the peg determines one out of the five first rows and then we add the sum of the symbols to that position. To test our hypothesis, we compute every position and see that there really is a free hole for the peg.

The sum (using the position in alphabetical order starting from zero) of the symbol sets: (BLUE, $25+22+26+7=78$), (RED, $9+7+1+2=19$), (GREEN, $7+2+7+26=42$), (PURPLE, $20+1+17+7=45$), (ORANGE, $3+17+1+20=41$). Then, the possible positions for each peg are:

Assuming this is correct, there are $6 \times (6-1) \times (5-1)^3 = 1920 < N < 6^2 \times 5^3 = 4500$ different combinations to try (handwavingly) mapping the colours to the rows. Maybe I made a mistake when computing the numbers (and the solution is distinct) or I am going down the completely wrong route.

EDIT: The message is binary in some encoding -- UTF-9?

EDIT2: The rows have 18, 14, 14, 14, 13, 15, 15, 5 and 15 pegs respectively. There are exactly 5 odd-parity rows. If the last column is the parity column, it should be filled with 100011111. However, the parity column could be any of several, so the solution is not really unique.

• I can tell you that, once Harold figured out the pattern, there was a distinct solution for which holes needed to be filled in. Oct 27, 2015 at 15:04
• @EngineerToast Maybe I'm thinking too much outside the box now, but does your avatar have something to do with this? :-) Nov 18, 2015 at 21:06

Well, based on all the hints and 2012rcampion's new picture, it looks like the pattern is

a qwerty keyboard.

Based on that, it looks like the five missing pegs are

two to fill in the "W", two to fill in the "E", and one to fill in the "T". Counting from the top left as (1,1) that would be pegs at (4,2) and (7,2) for W, (8,1) and (8,3) for "E", and (14,2) for "T".

The name was presumably relevant because of

Antonín Dvořák, which sounds like the Dvorak keyboard (but it was named after a different Dvorak!) The QWERTY keyboard was invented in the early 1870s by Christopher Latham Sholes.

• I couldn't tell if you posted before or after @2012rcampion edited their answer but you reference his picture as having given you the solution and their post includes more detail. They get the tick but you get +1. Nov 19, 2015 at 13:27
• This was before they gave their final answer - I wrote this when you still had the wrong name up. Also I was wrong about the location of the pegs, I didn't think about tying string between them and I was only going by the first row. Nov 19, 2015 at 14:09