PMC - The Box Mystery Cache

An old Winger song played on the radio as I turned the puzzle box over in my hands, examining it closely. It was beautifully carved, with gold leaf adorning its ebony surface in intricate hieroglyphics. It was part of a puzzle legacy that my father had inherited from his father, who in turn had inherited it from his father, and so on, passed down through the generations for three hundred years. Now upon my father's death it had been passed on to me.

It held a secret.

I turned one of the corners and instantly the cube transformed into a sphere. Another twist and it was a tetrahedron.

The hours passed as the box transmogrified into increasingly more complex shapes with each twist I applied to it. Its repertoire of forms seemed endless. As I was about to put it aside and retire for the evening, I gave the box one final twist. It transformed into a shape with four octagonal sides and a cross in the center. A hole opened in the cross and a small slip of paper fell onto my lap. Putting the box aside, I picked up the yellowed paper and unfolded it with trembling hands. On one side was a cipher. I pondered it for a while, then turned the paper over. On the other side it read:

Son, if you're reading this, then I am with you now in spirit only. The cipher on the back of this sheet was created by your grandfather. The box is my invention. Each generation modifies the puzzle in some way, either by changing it or by adding to it. The secret it conceals is just one piece of a larger puzzle whose other pieces are held by people you do not know. Together they reveal the location of an amazing treasure that was hidden long ago. It is the last of its kind. I don't know who these other people are. Through the generations their identities have been lost to us. The treasure was not meant to stay hidden forever, but to one day be found by those with the perseverance and fortitude to unravel the mystery. For years I have searched in vain for those who held the other pieces of this puzzle. Maybe you will have better luck than I did in finding them.

My eyes narrowed slightly under a knitted brow as I thoughtfully considered what I had read. Then I remembered a website where people exchanged clues to finding hidden treasures. Could it be that the others were already seeking me out as well? If so, I would add my puzzle piece to the others and maybe someday the treasure – the last of its kind – would be found.

You'll have to solve five puzzles to find this geocache. The first three are Boolean mazes – my contribution to the mystery. I'f you've never solved a Boolean maze before, visit "Cheese, That’s Nice", GC10X3N.

For the next two puzzles you must use some geometry. They are, to the best of my recollection, two of the shapes the box took as I tried to solve it.

The above cube is ten inches on each side. Begin by cutting off all eight corners (the dotted lines in figure 1 shows the cut on one corner), so that all the resulting equilateral triangles are the same size and touch each other exactly at their corners. Figure 2 shows the result. Drill a circular hole through the middle of the shape as shown in figure 3. Note that the hole is exactly wide enough to touch the triangle on all three sides.
What is the surface area of the above shape (Figure 3), rounded to the nearest whole number?

This cube is the same size as the first. Cut it on the dotted lines as shown, so that the sides form perfect octagons (all eight sides are the same length and all its angles are equal.) Figure 2 shows the result. Superimpose two of these shapes at right angles to get the shape formed in figure 3. Drill a circular hole through the middle as shown in figure 4. Note that the hole is exactly wide enough to touch all four inner corners of the cross.
What is the surface area of the above shape (Figure 4), rounded to the nearest whole number?

Lastly, you must decode the cipher that appeared on the back of the sheet:

DZOUL XZOUP IHJOHHA NZJTZZR ZDNP AUHYA J UFODA DZOUL THXZOH PMBSIG SEOMIS DGPMARB JLZAU SDMDBTW NSZIEE CZOKBI GSMIE ZWCMRDQ ULH QTAHB YMXMUE SMBHQSG ULH SOMICGK ULOZFJL ULH JZNIHD AKGCXBNQ IUAQC SIQG GGHGZ ENE HIJHA QO KPSM MGTE JEQM FWSBPWM CIRMNB JBLMUB ULH MPMYA CAMUK GCHWM BIKMQ ULH ZDNP ZULHO OFNH VA RHHY PZFO RDHHA ZXX ULH AUZDH ZD ULH NHXU

A = Subtract the sum of the first maze from the sum of the second maze. From this figure subtract the first 3 digits revealed by the cipher. To this add 1.
B = The fifth digit revealed by the cipher.
C = Subtract the area of the first shape from the sum of the second maze. Find the sum of the individual digits in your answer. From this subtract six.
D = Subtract the sum of the third maze from the area of the second shape. Find the square root of this figure. From this subtract 1.
E = The second digit revealed by the cipher.
F = The last digit revealed by the cipher.

The cache is located at:
N 40°37.ABC
W 75°11.DEF

The cache is a micro and contains a logbook only. BYOP

You can check your answers for this puzzle on Geochecker.com.

If you complete the puzzle, please don’t give the answer to anyone else. Let them experience the joy of working it out for themselves like you did.

PMC: PUZZLE MASTER'S CHALLENGE

This puzzle is part of a series of puzzles created by the greatest Puzzle Masters of the Mid Atlantic Region. There are a number of Puzzle Masters contributing to this series. Solve all of the Puzzle Masters' creations, follow the storylines, gather the clues and find the final. Will you accept the challenge?

Each puzzle is a unique work of art created and owned by each Puzzle Master/Puzzle Team. In each cache there will be a clue that you must gather and record. These clues will lead you to a final mystery cache located somewhere in the mid-Atlantic region. This series is designed to lead you on an epic adventure that will require Master puzzle-solving skills and extensive travel to unique locations. You must travel and log in at each cache in order to claim a find on the final. Due to the extensive time and effort put into this challenge, the cache can be done as a group but each member of the group must go to each cache site and sign each log. Dividing into sub groups and pooling your efforts will not be allowed.
 

PMC: THE PUZZLE MASTERS

Listed below are the owners and creators of each cache in the series.

 • CinderBankers
 • CondorTrax PMC - I Dislike Numbers
 • Dirty Bird and Big Nasty Brain PMC - Creative Confusion
 • EastVillageFamily PMC - Urban Renewal
 • Ekitt10 PMC - The Message
 • Frodo_Underhill PMC - Quick Brown Fox +-25
 • GALAP PMC - Uncle Buck's Cards
 • GerIRL PMC - Hibernia
 • Grunriese PMC - Flatlander
 • Hostanut PMC - The Order
 • M_and_W PMC - The Sun, Moon and Stars
 • mblatch and ericles PMC - S.E.T.I.
 • ODragon PMC - A Tribute to Caching
 • rehobch PMC - Clueless Again ?
 • Resolution PMC - Professor Stone
 • Vinny & Sue Team and MMammel PMC - Song of the Master Sun
 • we3girlsnaguy PMC - The Meeting House

AND THE FINAL.....