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Bongard Christmas Puzzles.... Mystery Cache

Hidden : 11/4/2003
Difficulty:
5 out of 5
Terrain:
3 out of 5

Size: Size:   regular (regular)

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Geocache Description:

A Christmas Puzzler for y'all. It's easy - just solve the 6 problems to get the cache co-ordinates!

The posted co-ordinates are NOT those of the cache location - they just give a general idea of the area.

OK, so where is the cache?
It's nearby. We're just not telling you where just yet. You have to work that out.
Well, we'll give you a clue: N51° ab.cde'...0° fg.hij' - we're not even saying which hemisphere it's in!

And how do I work it out?
Once a week, in the 6 weeks leading up to Christmas, we'll be posting a puzzle on this page. Solving the puzzle will yield a digit or two from the coordinates. By the 22nd of December 2003, you'll have all the coordinates you need.
It will probably be possible to deduce the location of the cache before the 6th (and possibly the 5th) puzzle is posted, so there are going to be extra-special presents in the cache for the first finder (hopefully before christmas!)

A puzzle? What kind of puzzle
A Bongard puzzle, to be precise, or at least puzzles based on the original Bongard puzzles. See Harry Foundalis' Research Page which explains them far better than I will attempt to.

Eh? What?
A Bongard puzzle is a cognitive-visual pattern-recognition puzzle. You have to work out the relationship or property that links a group of objects.
Here's an example:

Example Bongard puzzle


Each Bongard Puzzle has 6 boxes on the left and 6 on the right. There is a rule that describes why the boxes on the left belong with each other - there exists a common property that all six boxes share. There may also be a different rule/property for the boxes on the right, but usually that rule is "They don't share the same property as the ones on the left".
N.B. None of the right-hand boxes will adhere to the rule that defines those on the left. This will allow you to eliminate any patterns that you might spot for the left-hand side that aren't the correct answer.
 
So, in the example above, all the boxes on the left have 1 shape in them. But that can't be the rule, because there are boxes on the right (in this case all) that also fit that rule. The actual answer is of course that the shapes in the boxes on the left are all empty, and those on the right are filled in.
And that's a very easy one!

Right, so I've worked out the rule for a puzzle, now what?
We'll also give you a set of unsorted extra boxes at the bottom of each puzzle. You will have to sort them into two groups according to the rule, and this will yield a number or two, which will be explained.
 
The boxes at the bottom of each puzzle should be ignored until you've worked out the rule for the set of left and right boxes!

So what next?
Wait. We'll be posting the first Bongard puzzle shortly, and thereafter one each Monday morning until December 22nd 2003. The cache will physically be placed around the beginning of December, long before you'll be able to find it anyway.
 
After the New Year, we'll post encrypted hints for each puzzle to make it slightly easier.

How will I know I've got the digits correct?
You can email me (Huga) to check individual digits are correct, or to check if you've worked out the rule correctly.

What if I get stuck?
E-mail me (Huga) and I'll give you a clue. If you're really stuck you can ask for direct answers!


The Puzzles

Week 1


This week's puzzle will give you digit d
How to get the digit:
1) Work out the rule that separates the 6 squares in the left group from those in the right group.
2) Apply the same rule to the 12 squares in the the bottom group, so that you separate them into "left" and "right" along with the first 12 squares.
3) Once this is done correctly, you will find that all the numbers (the ones in the top corner of each square) are equally divided between "left" and "right" (so if there are 2 of a number, there'll be one on each side, if there are 4, there'll be 2 on each side), except for one number, which will be asymmetric and will only be "right" or "left", on one side. This number is the digit you're looking for, digit d.

Week 2


This week's puzzle will give you digit i
How to get the digit:
1) Same as last week. Work out the rule that links the 6 left-hand squares.
2) Apply this rule to the 12 squares in the the bottom group, so that you separate them into "left" and "right" along with the two pre-sorted groups.
3) Once this is done correctly, you will find that all the numbers (the ones in the top corner of each square) are equally divided between "left" and "right" (so if there are 2 of a number, there'll be one on each side, if there are 4, there'll be 2 on each side), except for one number, which will be asymmetric and will only be "right" or "left", on one side. This number is the digit you're looking for, digit i.

Please note that the numbers in the squares, their colours or their positions have nothing to do with the rule that defines the puzzle. They are just there for getting a coordinates out of the puzzle

Week 3


This week's puzzle will give you digits c and f
How to get the digits:
1) Same as last week. Work out the rule that links the 6 left-hand squares and not the 6 right-hand ones - discover their common property.
2) Apply this rule to the 12 squares in the the bottom group, so that you separate them into "left" and "right" along with the two pre-sorted groups.
3) Once this is done correctly, you will find that all the numbers (the ones in the corner of each square) are equally divided between "left" and "right" (so if there are 2 of a number, there'll be one on each side, if there are 4, there'll be 2 on each side), except for two numbers, which will be asymmetric and will only be "right" or "left", on one side each. These numbers are the digits you're looking for. The digit on the left side only is c and that on the right side only is f.

Please note that the numbers in the squares, their colours or their positions have nothing to do with the rule that defines the puzzle. They are just there for getting a coordinates out of the puzzle

Week 4


This week's puzzle will give you digits a and j
How to get the digits:
1) Kind of similar to start with: Work out the rule that links the 6 left-hand squares and not the 6 right-hand ones - discover their common property. Remember that the rule must fit all of the left-hand squares and none of the right-hand ones!
2) Apply this rule to the 12 squares in the the bottom group, so that you separate them into "left" and "right" along with the two pre-sorted "left" and "right" groups.
3) Once this is done correctly, You will find that you can make the names of two digits (i.e. a number between nought and nine) out of the letters that are grouped as "left". You may re-use letters between the names you make, but not within each name - for example if you only have one "n" you can't make "nine" but you can make "seven" and "one". The two numbers you're after are not the same!
The smaller of the two numbers you find is digit a and the larger is digit j.

Please note that the letters in the squares, their colours or their positions have nothing to do with the rule that defines the puzzle. They are just there for getting a coordinates out of the puzzle

Week 5


This week's puzzle will give you digits e and g
How to get the digits:
1) Kind of similar to last week's: Work out the rule that links the 6 left-hand squares and not the 6 right-hand ones - discover their common property. Remember that the rule must fit all of the left-hand squares and none of the right-hand ones!
2) Apply this rule to the 12 squares in the the bottom group, so that you separate them into "left" and "right" along with the two pre-sorted "left" and "right" groups.
3) Once this is done, collect the letters from all the boxes classified as "left". With these letters, you will be able to construct the names of two digits between nought and nine. You must use all the letters once and once only - so the letters ONETW could not make "one" and "two" since that would require reuse of a letter, and having just those five letters would indicate you've got the puzzle wrong. If you can't make the names of two digits without leftover letters or reuse of letters, then you'll have to think again...
The smaller of the two numbers you find is digit g and the larger is digit e.

Please note that the letters in the squares, their colours or their positions have nothing to do with the rule that defines the puzzle. They are just there for getting a coordinates out of the puzzle

Week 6


This week's puzzle will give you digits b and h
How to get the digits:
1) Work out the rule that links the 6 left-hand squares and not the 6 right-hand ones - discover the common property that the 6 left squares have in common. Remember that the rule must fit all of the left-hand squares and none of the right-hand ones!
2) Apply this rule to the 12 squares in the the bottom group
3) The number of boxes on the top row of the 12 "bottom" boxes that conform to the rule is digit b
4) The total number of the 12 "bottom" boxes that conform to the rule is digit h

Right, that's all the puzzles done, and all the digits acquired. We're still not going to tell you which hemisphere it's in, so you'll have to guess or work out the East/West bit for yourself. Good luck...
 
Huga and Wronskian

Additional Hints (Decrypt)

Arne Jner va Uregsbeqfuver. Gel gb xrrc jnez va gur anfgl jrngure bire gur srfgvir frnfba! [Clues for the puzzles] [Puzzle 1:] Obgu...? [Puzzle 2:] N cevzr rknzcyr [Puzzle 3:] Gel qenjvat n qvntbany yvar [Puzzle 4:] Vtaber gur erq funcrf pbzcyrgryl. [Puzzle 5:] Gvcf bs obggbz oenapurf ba rnpu fvqr bs rnpu 'gerr' [Puzzle 6:] Guvax zveebef.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)