MSIG 2011: Future Energy Institute MSIG 2011: Federal Espionage and Intelligence

Formulaz Solution

How It Works

Teams receive an assortment of cardstock squares (in 6 colors: red, orange, yellow, green, blue, purple) and pages with color labels. Example of empty grid scaffold: Formulaz_frame_red.pdf Example of assembled 5x5 color grid: Formulaz_grid_red.pdf

Teams' first task is to assemble each of the single color 5x5 large squares from the smaller squares; this can be done by realizing that both the rectangle pattern along the edge of each small square and the chemical symbols in adjacent squares will match. Teams will eventually realize that each color follows a very similar pattern, all the edging is identical, the only thing that changes between large squares are some of the specific chemical elements.

That's the easy part! Now for the puzzle...

Along with a scaffold for each of the separate colors, there is one more scaffold, that looks like this: Combined scaffold: Formulaz_combo_frame.pdf

This frame contains some super-useful information, namely that you are trying to create a bunch of molecules by mixing the individually colored compounds:

  • 1 HF
  • 1 KCl
  • 1 KF
  • 1 LiOH
  • 1 NaCl
  • 1 NO2
  • 1 NO3
  • 1 OH2
  • 1 PH3
  • 1 SH2
  • 1 SiO2
  • 1 SO3
  • 2 CO2
  • 2 HCl
  • 2 NaOH
  • 2 NH3

There are 20 molecules to make. There are also 20 edges with elements in each grid. Those facts, and the flavortext for the puzzle, combined with the fact that each single color grid has the same layout as all the others, hints at the fact that these 20 molecules can be made, one on each edge, by combining 25 total squares, one from each position in the grid, some of each color, into one multicolored grid. How exactly to do this follows...


You should refer to this, which is the final solution: Final formula solution You should view the black and gray boxes as what's happening on the edge of a square. Gray boxes are just where there's a rectangle pattern. Black boxes have a series of chemical elements on them. The one listed here is the "suffix" that I'll talk about now.

Each molecule that we're trying to make is composed of two parts, a prefix and a suffix. The suffixes are the same on every color grid and appear with a dash in front of them. They are always on one end, and they are always in the same place.

The available suffixes are:

  • -Cl
  • -F
  • -OH
  • -O3
  • -O2
  • -H3
  • -H2

If you're looking at the solution grid, you can see where each of the suffixes appear. Noting that each suffix always appears in the same place on every grid is important, because it gives you a starting place. For example, you can figure out that that HF molecule that you are trying to make has to be made in one of the two spots where the -F suffix appears in the grid.

Now how do we make prefixes?

The prefixes are made by matching up colored squares. We've noted that aside from the suffixes, the elements that appear on square edge are different. That's not COMPLETELY true though – every edge will also have one other element in common, and in the same place, with any of the adjacent squares from any color. And, in fact, the element that it has in common depends entirely on what colors are being matched up. The same two colors will always have the same element in common.

These prefix color matchings are:

  • red & orange: K
  • red & yellow: Na
  • red & green: Cl
  • red & blue: Be
  • red & purple: Ca
  • orange & yellow: Si
  • orange & green: O
  • orange & blue: F
  • orange & purple: Mg
  • yellow & green: Li
  • yellow & blue: N
  • yellow & purple: H
  • green & blue: S
  • green & purple: C
  • blue & purple: P

We now have all the information that we need to solve, and what follows is just a semi-long logic puzzle. For example, we know that we need to make HF. This means that on one of the -F edges, we need to match up a yellow and purple square. We can detail out all these requirements, and there's a unique solution to how the squares must be placed to satisfy every constraint.

One possible place to start:

  • In the top row, second column, there's a square that needs to be placed that has both a -Cl and and -H2 suffix.
    • Prefixes that we need to match with -Cl: K, Na, H
      • Colors that make up these prefixes: red, orange, yellow, purple
    • Prefixes that we need to match with -H2: O, S
      • Colors that make up these prefixes: orange, green, blue
    • The only color that appears in both lists is orange. Therefore, this square must be orange.
      • From there, we can determine that the 1st row, 1st column must be red, because it's the only color that orange can match up with over the -Cl edge.


Once the teams assemble the final grid, they must realize that the grid is an overlay of three colors - that is, purple represents both red and blue, green represents both blue and yellow, etc. Looking at the position of each color on the grid, they will see that the squares containing red are shaped like a 'D', the squares containing yellow are shaped like an 'N', and the squares containing blue are shaped like an 'A', giving the final answer, DNA.



Design Notes

The inspiration for this puzzle came from Kim wanting a way to play the game Mastermind with herself. How this puzzle at all relates to Mastermind in its current form is something that probably only Kim sees, but if you're interested in the explanation, you can email her here.

Construction Notes

150 squares per puzzle instance times 20 teams = 3000 cardstock squares to be cut out. Even with fancy papercutters at Kinko's with the precision required, this took... a long time.

GC Notes