3Y + 1W Conjecture – Collatz

A puzzle being solvable is only conjecture until it can be proved that it is possible.  Some folks use fancy shmancy mathematical proofs while the rest of us just bash our heads against it until it yields.  Or doesn’t, in which case, Q.E.D., it is relegated to the obviously unsolvable pile.

On the mathematically unsolvable pile lies the Collatz Conjecture.  The objective of this puzzle by German mathematician Lothar Collatz is to prove that any positive integer can be reduced to 1 in a finite number of steps where at each step the number is divided by 2 if it is even or multiplied by 3 and added to 1 if it is odd.  Yes, puzzlers aren’t the only community to dedicate time to solving capricious whims and fancies.

Taking inspiration from this unsolved mathematical puzzle, Dr. Volker Latussek transmogrified the 3n+1 transformation into 3Y+1W with the objective of reducing it to 1 restricted opening square space.

Collatz by Volker Latussek was Hendrick Haak’s exchange puzzle at the International Puzzle Party (IPP) 41.  It consists of 3 Y pentominoes and 1 W pentomino.  The objective is to place all 4 pentominoes in a 5x5 square.  To help you do this, a 5x5 tray is provided.  To further help you, there is a top on the tray to keep pieces from jumping out while you solve the puzzle.  A small slot in the side provides a convenient way to add the pieces to the tray.  Of course it is slightly offset to keep pieces from simply sliding out.

The puzzle is a nicely made ensemble of 3D printing and Laser Cut Acrylic.  The tray is 3D printed and the 4 pieces and top are laser-cut from Acrylic.  The top has 4 sizeable holes that can be used to manipulate the pieces within the tray.  And it can be slid off so that you can easily store the pieces in the tray so that they don’t fall out.  I came to the conclusion a while ago that all the packing puzzles that I print would have a sliding opening and I’m glad to see others embracing this as well.

So my solving experience went like this: This looks like it might work but I’ll be disappointed if it’s that easy.  Nope, the offset opening doesn’t allow that.  OK – maybe it’s like this, but it would still be too easy.  Nope #2.  Maybe I should think about it for a minute.  How about this – Yup.

It’s not difficult, but you do need to determine how the pieces interact with each other to get them correctly into the tray.  And I wasn’t disappointed!