by Benjamin L de Bivort
The team received a jigsaw puzzle and a sheet printed on card stock. Assembled, the jigsaw looked like:
This mysterious image shows graphs (in the mathematical sense of nodes-connected by edges) and mysterious big red dots.
The handout showed these dots, along with blanks and stubby black lines. In the handout, the dots were in alphabetical order. Teams who had the insight that a dot was a graph type could use this to help determine which graph types the puzzle used. It wasn't immediately clear which handout-dot went with which jigsaw-dot.
The alphabetical list of graph types (i.e., ordered as on the card stock sheet):
Solvers had to combine information from the handout and the assembled jigsaw: they had to determine which handout-dots corresponded to which jigsaw dots. With the correct configuration, guided by the stubby black lines, a solver can connect big red dots. Each connection passes through the drawing of a graph. The passed-through graph will be in the types of the two connected big red dots; e.g., connections from the INTEGRAL GRAPH red dot pass through integral graphs. Solvers can figure out which graph-type goes with a big red dot by looking at the little graph drawings and the dot's blanks.
On the handout, each red dot has one numbered blank among its blanks. By using the letters on those numbered blanks and ordering them, solvers get the message ANSWER IS THE SUBGRAPH OF VERTICES WITH DEGREE TWO K PLUS ONE. Interpreting this message, use the big-red-dot vertices, not the little-graph-image vertices.
Interpreting this message, use the big-red-dot vertices, not the little-graph-image vertices. Identify the big-red-dot vertices that have an odd degree (2k+1), and the subgraph they make up (all the edges between two odd-degreed big-red-dot vertices):
This is the solution: 📦, the package emoji.
The Graph TypesHere, the red dot graph types are listed by the number that appears in their blanks.