Bob’s 2010 Christmas Puzzle Card

(If you are looking for the 2011 card, please click here)

55 Elves Flexagon Puzzle

This year’s puzzle makes use of a flexagon— a device with several layers of paper that can be folded in certain ways to reveal faces other than the those that are initially visible. The two initially visible faces are shown below.

Two pdf files are provided for constructing the flexagon. The single-sided one can be printed on one side of an ordinary piece of paper. The double-sided one should be printed on both sides of paper, or card stock, and makes two copies of the flexagon. Construction instructions are included in the last page of each document.


Puzzle Instructions

There are three puzzles in this year’s card—two mazes and a word puzzle. The mazes both involve stepping from elf to elf until you reach the North Pole. All steps will move to an elf next to the one you are moving from, and the direction of your step will be completely determined by the elf you are leaving. However, depending on how you have folded the card, you may have more than one choice of elf to step to.

Before attempting the mazes, play around with the card to understand how folding it can reveal elves hidden inside. Depending on how the card is currently folded, you will be able to fold one of the edges of the card, either toward you (“in”) or away from you (“back”).

If you see Arplu, Hacla, Istof and Thedo across the top edge of the card, and fold the top and bottom edges into the middle, Yalla, Hadju, Rawnu and Hemoo will now be along the top. If you then fold the left and right edges into the middle, you'll have a shape like a plus sign with Hoofa and Ralon at the top. Folding top and bottom in then brings Ikero, Hesno, Tumpo and Herke to the top. And folding left and right in brings back Arplu and his gang.

Puzzle 1. The Eyes Have It

Starting at Okeno (the elf with the stylish gray hat), step elf-by-elf to the North Pole. The direction you must step is shown by the elves’ eyes. If an elf is looking left, you must step left, if he is looking down, you must step down, and so on. If an elf’s eyes are closed, you have reached a dead end.

For example, if you were visiting Opest, who is looking left, you could step to Vealu. But instead, you could fold the left edge back, then step from Opest to Spack.

When an elf directs you to step off the edge of the card, you must fold the card so that there is an elf ready to be stepped to.

The solution visits seven other elves, and uses three edge folding steps.

Puzzle 2. Hats Off To You

Starting again at Okeno, again step elf-by-elf to the North Pole. This time your direction is determined by the direction of the ball on each elf’s hat. Elves without hats are dead ends.

The solution visits thirteen other elves, and uses thirteen edge folding steps.

Puzzle 3. Have Your Elf a Merry Little Xmas

There are 55 elves on the card. Their names all appear in the classic poem “A Visit From St. Nicholas”, written nearly 200 years ago by Clement C. Moore.

While many people can recite the eight reindeer named in that poem (and recite them in order), few realize the names of 55 elves are also hidden within. For example, the phrase “like a bowl full of jelly” hides the name Keabo (but he isn’t one of the elves on the card).

The first challenge is to figure out the words each elf’s name comes from. The second challenge is to list the 55 elves in the order they occur in the poem.

Christmas Conundrums
  1. How does Santa deliver to all those houses in one night?
  2. How does Santa deliver gifts inside houses that don’t have a chimney?
  3. How does Santa eat all those cookies and not get sick?
  4. Does a Partridge in a Pear Tree really make a good Christmas Gift?
  5. Do Partridges eat pears?
  6. Why do sugarplums have their own fairies, but candy canes don’t?
  7. Why isn’t Keabo on the card?

(don't look if you don't want to see ‘em!)
Solution to The Eyes Have It
Solution to Hats Off To You
Solution to Have Your Elf a Merry Little Xmas
Answers to Conundrums