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Formula Deluxe

by Kevin Sun, Olga Vinogradova, Patrick Xia, and Steven Silverman


The flavortext, title, and images suggest that we are interested in Mario Kart 8 Deluxe ghosts. Specifically, we are interested in the Staff Ghosts. The word “Formula,” the fact that they are all numbered Equation (1), and the red italicized numbers hint that this might also be related to Formula 1.

This puzzle presents a series of “equations” to additionally clarify a couple things:

  1. (2nd equation) The year of F1 we are interested in is 2022.
  2. (3rd equation) c2 = cc = 200, so we are looking at the 200cc ghosts.
  3. (4th equation) We assume the speed of the racer is constant.
  4. (5th equation) However, the speed between laps can change. This makes sense because the staff ghost lap times are different for each lap. Note: the images in the integral bounds indicate the start of each lap in Mario Kart.

Now we can try to solve the unknown in each of the equations in the images. We first identify which course and staff ghost each image is, along with which lap it is on. The staff name fits in the blanks, which extracts a phrase for the next step: USE NO TURNS IN F ONE. This further confirms F1 if we haven’t noticed that connection yet.

Water ParkYUYAU
Mario CircuitJOOSTS
Toad HarborADRIENE
Shy Guy FallsANNEN
Rainbow RoadPEDROO
GBA Mario CircuitPITT
DS Cheep Cheep BeachMIZUHOU
GCN Dry Dry DesertCHRISR
N64 Royal RacewayDYLANN
3DS Music ParkMITSUI
3DS Piranha Plant SlideFRANKN
N64 Rainbow RoadFAUSTIF
Mute CitySHOO
Big BlueRIEE

Next, we can solve the equations.

Using the first image as an example, a full lap from the starting lights to when the “⅔” marker appears is defined as length 3337. We know that the image is 5.496 seconds into the lap and we can find the total time of the first lap as 28.882 seconds by looking up a video of the staff run. Therefore we can calculate the “?” distance traveled to the current point as (5.496/28.882) * 3337 = 635.

Next we have to notice that the given red lengths are also the lengths of F1 circuits from 2022, and that F1 circuits always have turns labeled with numbers. The circuit referenced by the first image is Circuit de Monaco. Here, we need to use the first equation which tells us to measure from the checkered line. Estimating 635m into the track from the checkered line gets us to the third turn. It is easiest to measure distance with the Google Maps satellite view and using the right-click→measure distance tool. Doing this for each of the tracks, we can calculate the turn number and subsequently convert the turns into letters (1=A, 2=B, etc). Finally, sorting the tracks when they appeared in the 2022 F1 circuit yields the puzzle answer CAR OF DISTINCTION.

The table below summarizes this information. The calculation is defined as (time to destination/total lap time) * (lap distance).

Puzzle orderF1 CircuitMarioKart circuitCalculation (m)Turn #Letter
1Circuit de Monaco Water Park(5.496/28.882) * 3337 = 6353C
13Baku City Circuit N64 Rainbow Road(0.680/21.633) * 6003 = 1891A
16Circuit Gilles-Villeneuve Big Blue(29.313/47.666) * 8722 = 536418R
12Silverstone Circuit 3DS Piranha Plant Slide(31.974/37.071) * 5891 = 508115O
4Red Bull Ring Shy Guy Falls(21.794/34.857) * 4318 = 27006F
11Circuit Paul Ricard 3DS Music Park(7.030/33.679) * 5842 = 12194D
5Hungaroring Rainbow Road(24.825/39.554) * 4381 = 27509I
14Circuit de Spa-Francorchamps Mute City(31.697/32.875) * 7004 = 675319S
15Circuit Zandvoort GCN Baby Park(12.743/19.053) * 8518 = 569720T
9Autodromo Nazionale di Monza N64 Royal Raceway(25.035/35.972) * 5793 = 40329I
6Marina Bay Street Circuit GBA Mario Circuit(18.163/25.4) * 5063 = 362014N
10Suzuka International Racing Course GCN Sherbet Land(6.442/33.448) * 5807 = 11183C
8Circuit of the Americas GCN Dry Dry Desert(35.695/36.744) * 5513 = 535620T
2Autódromo Hermanos Rodríguez Mario Circuit(18.655/28.569) * 4304 = 28109I
3Autodromo José Carlos Pace Toad Harbor(34.010/36.081) * 4309 = 406215O
7Yas Marina Circuit DS Cheep Cheep Beach(25.816/29.49) * 5281 = 462314N

Authors' Notes

The first version of this puzzle involved even more image ID. Each extracted letter needed three images and a total of five screenshot IDs among them. By getting the positions in the courses these screenshots were taken you could deduce the location of the final Mario Kart image and map it to an F1 turn number.

We spent a decent bit of time playing around with how to make the image ID more clear, but thankfully testsolvers were as annoyed by the obscene amount of data collection as we were and the puzzle was revised to the current version. Using the ghosts in the final puzzle came from one of these failed testsolves. We could scrub numerical data from the screenshots with relative ease (and tedium). However scrubbing the ghosts from the Mario Kart images was non-trivial which meant we might as well use them.

Examples of overlaid screenshots: