Solutions for Act V Scene 3 - Six Sided

The coloured dots and fold lines suggest that this is a construction puzzle, so the first step is to cut out each rhombus. But how do we put the pieces together?

There are a few key things to notice:

  • Two triangles have no dots, and are presumably special in some way
  • The two pairs of dots between the two triangles of any single piece are the same colour
  • Most importantly, every red triangle has a corresponding blue triangle having the same three coloured dots but in reverse orientation

The intuitive step is to realise that each red-blue triangle pair is to be glued back-to-back, such that their dots coincide. Doing so produces a straight double-sided strip of triangles, with two triangles unpaired at the ends and every three consecutive triangles having the same coloured dot where they meet.

(pictured here is a prototype - the actual puzzle had a few cosmetic changes)

The letters don't tell us much, so there must be more to do! We've used the dots, but we haven't used the blue solid lines and red dashed lines yet. By convention, dashed lines indicate valley folds and solid lines indicate mountain folds. Performing the valley folds first, then the mountain folds and gluing the two end triangles together produces this:

We have made a hexahexaflexagon! Not only does it have six sides (i.e. looks like a hexagon), it also has... six sides (like sides of a sheet of paper)! Although only two sides are initially visible, pinching the corners allows the centre to open up and reveal another side.

Flipping through the flexagon, we note that each number from 1 to 6 appears on exactly one face.

Taking each numbered triangle as a first letter and arranging the words by numerical order, we get SIX VS' MAKER TERRY'S SHAPES ACTION GAME. This is a reference to the game Super Hexagon, made by Terry Cavanagh of VVVVVV fame.

Design notes:

Internally, this puzzle was Folding Conundrum 2, alluding to another flexagon puzzle from the 2009 ΣUMS hunt. But calling it that would have been too much of a hint for those familiar with the original puzzle!

Although two triangles were intentionally left undotted to indicate that they were to go at the ends, in actual fact any pair of triangles could have served this purpose. However, having all triangles dotted would likely have led to the idea of forming a closed ring out of the strip, instead of folding first and treating the end triangles as tabs.

"SIX VS'" was chosen rather than "VVVVVV" as the sheer number of V's would have been far too suspicious.

The answer is: superhexagon