Press enter to skip to main content.

Solution: Elementary

Written by Nathan Sheffield, Ella Sheffield, and Adeline Wong

There are two main ahas necessary for the completion of this puzzle. The first is the connection to the board game Scotland Yard, which is a game that involves tracking a criminal around a map of London. Transportation lines between stations on this map are denoted as "bus", "train", "taxi", and "ferry" - the same methods of transportation used in this puzzle. (If solvers don't have a copy of Scotland Yard on hand, there are a number of versions of the map available online. The one found here is of particularly high quality.)

(Click to enlarge.)

The chain of transportation methods used is enough to uniquely identify the path that the criminal takes, but occasional descriptions of landmarks have been added to make the logic slightly easier. (See the appendix for the full logical solution.) This is the final unique path:


(Click to enlarge.)

The second aha in this puzzle is that each description of a crime corresponds to a death in an Agatha Christie novel - specifically, to someone dying from poison in an Agatha Christie novel. (Knowledgable solvers will recognize that Agatha Christie gained her knowledge of poisons by working as a pharmacist - which in England is called a chemist. The description of the killer matches her.)

The flavortext suggests that finding the methods of death is important, so solvers can begin to assemble a list of poisons. Each crime is also committed at a specific station from the Scotland Yard board; knowing the full path allows us to assign station numbers based on the locations given in the incident reports. The list that the solvers assemble may look like this:

87The Lemesurier InheritanceFormic acid
86One, Two, Buckle My ShoeAdrenaline and novocaine
85Triangle at RhodesStrophanthin
38The Coming of Mr QuinStrychnine
14The Big FourYellow Jasmine
67Murder in MesopotamiaHydrochloric Acid
112The House of Lurking DeathRicin
101Hickory Dickory DockMedinal
81The Herb of DeathDigitalis
18The Thumb Mark of St. PeterAtropine
75The Tuesday Night ClubArsenic
45Sad CypressMorphine hydrochloride
77The Chocolate BoxTrinitrin

At this point the solvers can return to the flavor text about a "deeper element hidden within her criminal methods", and realize that they have a series of numbers that are all underneath 118. Each of these numbers corresponds to an element with a two letter abbreviation. In each of the poisons, the two-letter abbreviation indicated by the element number appears separated by one letter. That letter can be extracted, and the list reordered by case number to form the final answer: TEMPLE STATION.

Case No.StationBookElementPoison
118The Thumb Mark of St. PeterArgon (Ar)ATROPINE
2101Hickory Dickory DockMendelevium (Md)MEDINAL
314The Big FourSilicon (Si)YELLOW JASMINE
567Murder in MesopotamiaHolmium (Ho)HYCROCHLORIC ACID
686One, Two, Buckle My ShoeRadon (Rn)ADRENALINE AND NOVOCAINE
775The Tuesday Night ClubRhenium (Re)ARSENIC
838The Coming of Mr QuinStrontium (Sr)STRYCHNINE
981The Herb of DeathThallium (Tl)DIGITALIS
1077The Chocolate BoxIridium (Ir)TRINITRIN
11112The House of Lurking DeathCopernicium (Cn)RICIN
1287The Lemesurier InheritanceFrancium (Fr)FORMIC ACID
1385Triangle at RhodesAstatine (At)STROPHANTHIN

Author’s Notes

Ella: When we started writing this puzzle, I enjoyed the game Scotland Yard. That was one of the reasons behind the idea towrite a puzzle about it! But I think it will be some time before I play this game again.

The truth is, this puzzle was scrapped once in the process of making this hunt, because the original draft used the same "numbers in the book title" mechanic for extraction that the round 1 meta did. You're looking at the reanimated corpse of this puzzle - and it gave us about as much trouble as necromantic abominations tend to give their creators.

The reason that I came back to this puzzle, at least, is because I really loved the theming. I thought the mechanic was fun, especially once I hit upon this idea for extraction, but really what sold me was the puzzle framework. Any Agatha Christie fan knows that she got much of her poison expertise by working as a pharmacist - also known, in Britain, as a chemist. Describing Christie as a mad scientist running around London killing all her own book characters gave me great pleasure. The path to this particular theming wasn't exactly linear, but I believe I would describe it as uniquely constraining. The answerphrase was too good to pass up for my idea of a Scotland Yard puzzle, and Nathan and I hit upon the idea of finding a unique path through the board very quickly. The mystery novels came second, and in the original draft we used books from other famously prolific mystery authors as well, such as Arthur Conan Doyle and Dorothy Sayers. I was glad to reduce this to one author, for elegance, but it was another constraint on our choices. We toyed with a number of options for extraction originally, but the range of path numbers lent itself well to using elements, so we went with that. The first draft also differed notably from the final version in that the path was only 13 steps long, one for each letter of extraction. Simpler times.

See, when we finally made the decision to scrap this puzzle, it was after a long time of Nathan and I trying and failing to get alternative mechanics to work - so what a reasonable person might assume is that, upon coming back to the puzzle, we tempered our expectations and tried to make the puzzle more reasonable to construct. Well, nope. We made it harder.

When I proposed the extraction mechanic, with hiding element abbreviations in Christie poisons, I was genuinely amazed that we even managed to get all the letters out of it, let alone expect that we could actually construct a working path. I'd expected to be back at the drawing board in no time. But I underestimated the stubborness of everyone involved in writing, especially Nathan, who should get huge kudos for being the one to actually do the coding and logical legwork needed to find a unique path. During pathfinding, we had to contend with, among other things, the fact that there are two slightly different versions of this board in existence, and with the fact that the beautifully clean map with a corresponding adjacency matrix that we found on github had an incorrect connection. So we had to make sure that our puzzle worked no matter which version of the map solvers were using. We started referring to Elementary as "the puzzle that must not be named" or just "That Puzzle" among ourselves as everyone slowly went insane.

And yet! Somehow we emerged on the other side with a working puzzle! And it is a puzzle that I am very proud to be partly responsible for. We had many back and forth discussions about flavortext cluing and nerfing the logic to various degrees, but in the end I am pleased with the difficulty we landed on. I hope that it is sufficiently mind-bending that Agatha herself would approve.

Adeline: I got drafted into this puzzle during the "this logic is cool, but we need a new extraction" phase, so my original contributions were (a) a bunch of spreadsheet-formula tables involving elements and numbers, and (b) a pirated copy of a book containing a list of every single poison used in an Agatha Christie novel or short story. Most of my further contributions consisted of watching in horror as Nathan conducted his eldtritch math to find the ever-longer paths that fit our extraction constraints, and extended Discord calls during which Ella and I derived and rederived the whole path from scratch, just to make sure it worked.

And it was...weirdly fun? I can actually see the appeal in sitting down over one of these during a hunt and churning out the whole thing, which is something I hadn't experienced in a logic puzzle before. We'll see if I still feel this way next time I solve a hunt, or if this is just some strange Londoner version of Stockholm syndrome.

Unrelated anecdote: at one point during the long process of writing this puzzle, I showed up unannounced at a quizbowl tournament intending to surprise Nathan. When the packet was over, he didn't even wait to walk over to me before shouting, "There's a path!" And somehow I did, in fact, immediately know what he was talking about.

Appendix: Path Logic

The first thing we observe is that the ferry locations restrict things significantly. There are only two ferry stops that are also bus stops, so immediately we know that the second location must be either 108 or 157.

From here, the only other places that the ferry can travel to are 194 and 115, regardless of where we start.

At this point we know we must be two taxis away from a train station. There are no train stations within two taxis of 194, so that is ruled out. The only way to get to a train station in two taxi rides from 115 is by going to 126 and then to 140. [This is right by Old Scotland Yard on the board :)]

The only clearly identifiable "financial institution" on the map is the Bank of England, at stop 89. The only way to get there in two train rides is by travelling to 128 and then to 89.

At this stage, the possible paths we can take begin to branch out, so we may find it more helpful to start working backwards from the start. We take a train into our starting location, which is also a bus ride away from our first ferry station. The only train station within a bus ride from either 157 or 108 is 185 (reachable from 157).

We now have two ways to take a train into 185, which connects both to 153 and to 128. However, we know from earlier that we visit 128 at a different point in the path, so this just leaves 153.

To get to 153, we know we had to take three buses, the first of which was directed southeasterly. Tracing out potential bus paths, we see that we can entirely rule out a path through 154. The options we are left with for the three-bus sequence are 58-77-124-153, 123-165-180-153, 176-190-184-153, and 165-180-184-153. For the next step in our logic, we are only concerned with the first in each of these sequences.

The sequence used to get to the chain of buses is a series of four taxis that starts from a train station. After some taxi counting, we can conclude that our possible options for the train station are 74, 93, 46, 163, and 111. Note that this rules out both 176 and 165 as starting locations, so we can remove their bus chains from the list of possibilities.

There seem to be a lot of possibilities now! However, we know that the suspect took two train rides to get to this point, and that the intermediate train station was at the corner of a park. This allows us to narrow things down. We can rule out 93 and 46 as the starting locations because they do not connect to any station at the corner of the park. We also rule out any path that crosses through 153, because we know we have to visit it later. This leaves us with just 46 and 111 as possible intermediate train stations, with 1, 13, 79, and 67 as potential pre-park-corner locations for this sequence.

Buckle in for some taxi counting now! To get to this train station, we must take a sequence of seven taxis that begins at a different train station. We also know that at least one of the first five of these taxis must cross a body of water. If our destination is 1, we must have started the sequence at 93, because we cannot visit 74 twice. There is no way to cross a body of water from a train station to end at 13, so we can rule that out entirely. To get to 79, it is possible to have started at 1, crossing a body of water between 9 and 20. We can also rule out 67 for the same reason as 13, so our only possible starting train locations are 93 and 1.

The previous mode of transportation was also a train, which once again leaves us with two options of places to be: 79 and 46.

At this point we want to be restricting our potential train stations. We can return to the beginning part of our path, where the suspect takes two taxis and a bus, and then 7 taxis to arrive at a train station with a royal name. The only stations on our map that have royal names are King's Cross at 13 and Victoria Station at 153. We know that we must visit 153 later, so this restricts us to 13.

We are now 5 buses away from another train station. This unfortunately still leaves us with many options: 46, 79, 67, 89, 111. However, if we rexamine our potential paths in the second half of our logic, we see that either option must use both 46 and 79. So we are left with either 67, 89, or 111.

Our next train ride expands our options again. We can now be at 11, 89, 67, or 163.

From one of these train stops, we must take four taxis to end at a bus station, and one of the latter two taxis must pass behind a gallery. Our gallery options are the Tate Britain, the Tate Modern, the National Gallery, and the British Museum. We can rule out the British Museum because there is no way to pass behind it at the correct step and end up at a bus station, and we can also rule out both Tate galleries, because there is no way to reach the Tate Britain, and no way to pass behind the Tate Modern. This means that our path must take us past the National Gallery, which can only be the path of 67-111-112-100-101-82. This also disambiguates our bottom section, because we have now visited 67. This allows us to lock down our bottom train sequences! The path from 93 to 46 has only one correct solution, and that solution disambigautes the two options for 74 to 58, so this leaves us with an ending sequence of 79-93-92-73-57-43-18-8-1-46-74-75-59-45-58-77-124-152-185, with 185 as our overall starting location.

Looking back at our path from 82, we must take a bus, which can only go to 65 because we've already visited 100, 140, and 67. From here, we must take four taxis, one of which is returning to its previous location, to reach either 78 or 63. With the backtrack, we cannot reach 78, which locks us down at 63. Our only way to get from 65 to 63 with doubling back is through 64-81-64-63.

We're almost there! Knowing that we can't visit 65 allows us to disambiguate our path between 13 and 67 to be 13-14-15-41-52-67.

To get to 13, we must have taken a chain of 7 taxis from a bus stop that we don't visit anywhere else. This gives us the options of starting this sequence at 3, 23, 22, 86, or 102. 3, 22 and 23 clearly will not connect to 89 in two taxis and a bus, so we are left considering 102 and 86.

At this point, the only thing left to do is to connect 89 to 86 or 102 in two taxis and a bus. There is no way to get to 102 this way, which leaves us with the unique chain of 89-88-87-86. And that is the final part of our path!

Note that this is not the only way to work out the logic, it is simply the way that the writers of this puzzle rederived it when writing the solution. Your deductions may have been different! Regardless, you should end up with the following path: 185-157-115-126-140-128-89-88-87-86-103-85-68-51-38-24-13-14-15-41-52-67-111-112-100-101-82-65-64-81-64-63-79-93-92-73-57-43-18-8-1-46-74-75-59-45-58-77-124-153.

trainfinancial institution89taxi
taxiCase 1287bus
busCase 686taxi
taxiCase 1385taxi
taxiCase 838taxi
taxitrain station with royal name13bus
busCase 314bus
busCase 567train
taxiCase 11112taxi
taxione of these next 2 taxis passes behind a gallery100taxi
taxiCase 2101taxi
taxiCase 981taxi
taxiback to prev location after having visited everywhere adjacent64taxi
taxiat least one of these 5 taxis crosses a body of water92taxi
taxiCase 118taxi
traincorner of park46train
taxiCase 775taxi
taxiCase 445taxi
busCase 10 (incoming southereasterly-bound)77bus