Solution to Two Heads are Better than One

by Oliver Kosut and Andrew Thomas

This is a "Siamese twins logic puzzle", along the same lines as the Siamese twins crossword puzzle. The 19 clue pairs divided by '/' make up two logic puzzles following the same set of rules. In each clue pair, one clue contributes to one logic puzzle and one to the other. To solve the puzzle, the proper way to divide the clues must be determined, as well as the solutions to the puzzles themselves. The two solutions are as follows (a possible chain of logic to solve them is given below):

AliceMicro-Goomba2pmNot severed
BobDancing Spear Guy4pmSevered
CarolBlooper Nanny3pmSevered
DavePiranha Plant5pmSevered
EveDark Goomba1pmNot severed
FrankGangantua Koopa Troopa6pmSevered
GloriaElectrogoomba9pmNot severed
HenryBeach Koopa7pmSevered
IreneKoopa Paratroopa8pmSevered

AliceDark Goomba8pmSevered
BobKoopa Paratroopa7pmSevered
DavePiranha Plant9pmSevered
EveBeach Koopa2pmSevered
FrankBlooper Nanny6pmNot severed
HenryGargantua Koopa Troopa3pmNot severed
IreneDancing Spear Guy1pmSevered

As suggested by the way Bowser displays his executed, the answer is found by indexing into the species names by the execution times, in alphabetical order by first name, and only for creatures whose heads were fully severed. Doing so yields CONNOR the one solution and MACLEOD for the other. Therefore the answer is CONNOR MACLEOD, someone who was involved in nearly as many beheadings as Bowser.

One possible sequence of logic to solve the puzzle is as follows. In particular, we show how to determine which sets of clues belong together. We refer to the 19 clue pairs by number from the order in which they are given in the puzzle. 1a indicates the first clue pair and the first clue in the pair, 1b indicates the second. When we write 2b6b18b/2a6a18a, this means that we have concluded that the clues on the left belong together, and the clues on the right belong together.

Consider clue pairs 3, 4, 9, 11, 16. The following sets of clues are together inconsistent:

This leaves the only possibility as 3b4b9b11b16a/3a4a9a11a16b.

Since 7a and 7b are identical, we may arbitrarily place them as 3b4b9b11b16a7a/3a4a9a11a16b7b.

2a is inconsistent with 6b, and 2b with 18a. Therefore we have 2b6b18b/2a6a18a.

Now we want to combine these two chunks. One possibility is 3b4b9b11b16a7a,2a6a18a/3a4a9a11a16b7b,2b6b18b. The right-hand state, from 18b, has the non-Koopa non-Goombas adjacent. Since from 3a, Alice is directly between Bob and Dave, and from 6b, Bob is not a Koopa or a Goomba, by 1a or 1b Alice must be a Piranha Plant and Dave a Goomba. This is inconsistent with 19b, so we apply 19a. The execution order must therefore include: Blooper Nanny, Dancing Spear Guy (Bob), Piranha Plant (Alice), Micro/Dark Goomba (Dave), Beach Koopa, Gargantua Koopa Troopa/Koopa Paratroopa This is inconsistent with both 15a and 15b. Therefore we have 3b4b9b11b16a7a2b6b18b/3a4a9a11a16b7b2a6a18a.

By 2a, Alice is the Dark Goomba, which is consistent with 1a not 1b, so we have 3b4b9b11b16a7a2b6b18b1b/3a4a9a11a16b7b2a6a18a1a.

12a is inconsistent with 11b and 10a with 11a, so we have 3b4b9b11b16a7a2b6b18b1b12b10a/3a4a9a11a16b7b2a6a18a1a12a10b.

8a is inconsistent with 10a, giving 3b4b9b11b16a7a2b6b18b1b12b10a8b/3a4a9a11a16b7b2a6a18a1a12a10b8a.

In the right-hand state, 3a and 6a imply that Bob was executed at 7pm, Alice at 8pm, and Dave at 9pm. From 10b, Irene was executed before 4pm. These facts together are inconsistent with 13b, so we have 3b4b9b11b16a7a2b6b18b1b12b10a8b13b/3a4a9a11a16b7b2a6a18a1a12a10b8a13a.

In the right-hand state, the clues so far show that the Piranha Plant was executed at 9pm, which is inconsistent with 19a, so we have 3b4b9b11b16a7a2b6b18b1b12b10a8b13b19a/3a4a9a11a16b7b2a6a18a1a12a10b8a13a19b.

In the left-hand state, the Blooper Nanny was executed at 3pm, which is inconsistent with 15b, giving 3b4b9b11b16a7a2b6b18b1b12b10a8b13b19a15a/3a4a9a11a16b7b2a6a18a1a12a10b8a13a19b15b.

Consider clues relating creature names to execution times in the current left-hand state. Eve was executed at 1pm, Carol at 3pm, and Henry at 7pm. From 1b and 19a, the creature executed at 5pm can only be Alice or Dave. From 15a, the Gargantua Koopa Troopa, which we know to be Frank, is executed before 7pm. 12b eliminates all possibilites except that Gloria is executed at 9pm. Applying 13b with these facts uniquely relates all names and execution times.

In the left-hand state, the creatures executed at 1pm and 2pm did not have their heads severed, which is inconsistent with 5b, giving 3b4b9b11b16a7a2b6b18b1b12b10a8b13b19a15a5a/3a4a9a11a16b7b2a6a18a1a12a10b8a13a19b15b5b.

14a is now inconsistent with the left-hand state, giving 3b4b9b11b16a7a2b6b18b1b12b10a8b13b19a15a5a14b/3a4a9a11a16b7b2a6a18a1a12a10b8a13a19b15b5b14a.

17a is now inconsistent with the left-hand state, giving the complete clue breakdown: 3b4b9b11b16a7a2b6b18b1b12b10a8b13b19a15a5a14b17b/3a4a9a11a16b7b2a6a18a1a12a10b8a13a19b15b5b14a17a.