from Caxton C. Foster:
There is an old New England story about the sailor who decided to retire from the sea. He said he was going to put an oar over his shoulder and walk inland until someone asked him what he was carrying.
Last winter I was on the island of Antigua in the West Indies. A taxi driver asked me what I did and I replied that “I teach about computers”. When he said “What are they?” I knew right away that was where I wanted to settle down.
I used to have that book:
Content Addressable Parallel Processors.
That quote was right there on page 1 in the first paragraph. Here go ahead and take a free sniff (with a log=on of course!)
https://archive.org/details/contentaddressab0000fost/mode/2up- Code: Select all
Content Addressable Parallel Processors
—————————————————————-
Publisher Van Nostrand Reinhold
Publication date January 1, 1976
Edition First Edition
Language English
Print length 233 pages
ISBN-10 0442224338
ISBN-13 978-0442224332
Item Weight 1.3 pounds
Sometimes I feel that way about Sudoku! But NOT today. Today I am no longer totally overwhelmed by
6,670,903,752,021,072,936,960. Now, I am just slightly overwhelmed by the
ED# =
5,472,730,538. The number of Essentially Different solutuions. Gordon F. Royle would say there are
equivalence classes within the
ED I have heard there are
416 of these equivalence classes. However, all is not so simple from there!
Instead I am going back to the
ED. There are many ways to sort, list, catalog them. The
minlex way seems the most popular. But there are ED# of them! So I figured out that “Geany”, one of my linux text editors could handle a text file of this size. A 1 billion long list composed of 81-char lines of zeros. That way, I figured 6 files of that size should hold them.
Supposedly in the past there were physical memory storage devices being sent to “certain people” with the mysterious
ED on it. Of course this is too
primitive to do now! So the
gurus found ways to compress that data. One of the gurus in that science was
Glenn Stephen Fowler of AT&T Labs. There are others!
I had discovered a way to shorten an 81-char line to 48 chars. I actually programmed it in Python. I post it at the end. Here is the article that told me how:
So, here I am in my
naivete wondering about those 81-char lines in the list of
ED: What would happen if those 81-char lines got shortened to 48 chars? Then perhaps this catalog is broken up into 6 1 billion long text files. Each of these six files got compressed by the readily available
zip file process. What would be the size of these files? Would they be short enough to say get posted on the
OEIS!
https://oeisf.org/Am I crazy?
codec_support.py- Code: Select all
'''
codec_support.py
2021-05-05 Wed
'''
BLOCK_LIMITED_PEERS = {
20: [0, 1, 2, 9, 10, 11, 18, 19],
23: [3, 4, 5, 12, 13, 14, 21, 22],
47: [27, 28, 29, 36, 37, 38, 45, 46],
53: [33, 34, 35, 42, 43, 44, 51, 52],
77: [57, 58, 59, 66, 67, 68, 75, 76],
80: [60, 61, 62, 69, 70, 71, 78, 79]
}
PEERS = {
0: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 27, 36, 45, 54, 63, 72],
1: [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 28, 37, 46, 55, 64, 73],
2: [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 29, 38, 47, 56, 65, 74],
3: [0, 1, 2, 4, 5, 6, 7, 8, 12, 13, 14, 21, 22, 23, 30, 39, 48, 57, 66, 75],
4: [0, 1, 2, 3, 5, 6, 7, 8, 12, 13, 14, 21, 22, 23, 31, 40, 49, 58, 67, 76],
5: [0, 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 22, 23, 32, 41, 50, 59, 68, 77],
6: [0, 1, 2, 3, 4, 5, 7, 8, 15, 16, 17, 24, 25, 26, 33, 42, 51, 60, 69, 78],
7: [0, 1, 2, 3, 4, 5, 6, 8, 15, 16, 17, 24, 25, 26, 34, 43, 52, 61, 70, 79],
8: [0, 1, 2, 3, 4, 5, 6, 7, 15, 16, 17, 24, 25, 26, 35, 44, 53, 62, 71, 80],
9: [0, 1, 2, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 36, 45, 54, 63, 72],
10: [0, 1, 2, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 28, 37, 46, 55, 64, 73],
11: [0, 1, 2, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 29, 38, 47, 56, 65, 74],
12: [3, 4, 5, 9, 10, 11, 13, 14, 15, 16, 17, 21, 22, 23, 30, 39, 48, 57, 66, 75],
13: [3, 4, 5, 9, 10, 11, 12, 14, 15, 16, 17, 21, 22, 23, 31, 40, 49, 58, 67, 76],
14: [3, 4, 5, 9, 10, 11, 12, 13, 15, 16, 17, 21, 22, 23, 32, 41, 50, 59, 68, 77],
15: [6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 24, 25, 26, 33, 42, 51, 60, 69, 78],
16: [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 25, 26, 34, 43, 52, 61, 70, 79],
17: [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 35, 44, 53, 62, 71, 80],
18: [0, 1, 2, 9, 10, 11, 19, 20, 21, 22, 23, 24, 25, 26, 27, 36, 45, 54, 63, 72],
19: [0, 1, 2, 9, 10, 11, 18, 20, 21, 22, 23, 24, 25, 26, 28, 37, 46, 55, 64, 73],
20: [0, 1, 2, 9, 10, 11, 18, 19, 21, 22, 23, 24, 25, 26, 29, 38, 47, 56, 65, 74],
21: [3, 4, 5, 12, 13, 14, 18, 19, 20, 22, 23, 24, 25, 26, 30, 39, 48, 57, 66, 75],
22: [3, 4, 5, 12, 13, 14, 18, 19, 20, 21, 23, 24, 25, 26, 31, 40, 49, 58, 67, 76],
23: [3, 4, 5, 12, 13, 14, 18, 19, 20, 21, 22, 24, 25, 26, 32, 41, 50, 59, 68, 77],
24: [6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 33, 42, 51, 60, 69, 78],
25: [6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 34, 43, 52, 61, 70, 79],
26: [6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 44, 53, 62, 71, 80],
27: [0, 9, 18, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 54, 63, 72],
28: [1, 10, 19, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 55, 64, 73],
29: [2, 11, 20, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 56, 65, 74],
30: [3, 12, 21, 27, 28, 29, 31, 32, 33, 34, 35, 39, 40, 41, 48, 49, 50, 57, 66, 75],
31: [4, 13, 22, 27, 28, 29, 30, 32, 33, 34, 35, 39, 40, 41, 48, 49, 50, 58, 67, 76],
32: [5, 14, 23, 27, 28, 29, 30, 31, 33, 34, 35, 39, 40, 41, 48, 49, 50, 59, 68, 77],
33: [6, 15, 24, 27, 28, 29, 30, 31, 32, 34, 35, 42, 43, 44, 51, 52, 53, 60, 69, 78],
34: [7, 16, 25, 27, 28, 29, 30, 31, 32, 33, 35, 42, 43, 44, 51, 52, 53, 61, 70, 79],
35: [8, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 42, 43, 44, 51, 52, 53, 62, 71, 80],
36: [0, 9, 18, 27, 28, 29, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 54, 63, 72],
37: [1, 10, 19, 27, 28, 29, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 55, 64, 73],
38: [2, 11, 20, 27, 28, 29, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 56, 65, 74],
39: [3, 12, 21, 30, 31, 32, 36, 37, 38, 40, 41, 42, 43, 44, 48, 49, 50, 57, 66, 75],
40: [4, 13, 22, 30, 31, 32, 36, 37, 38, 39, 41, 42, 43, 44, 48, 49, 50, 58, 67, 76],
41: [5, 14, 23, 30, 31, 32, 36, 37, 38, 39, 40, 42, 43, 44, 48, 49, 50, 59, 68, 77],
42: [6, 15, 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 51, 52, 53, 60, 69, 78],
43: [7, 16, 25, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 51, 52, 53, 61, 70, 79],
44: [8, 17, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 51, 52, 53, 62, 71, 80],
45: [0, 9, 18, 27, 28, 29, 36, 37, 38, 46, 47, 48, 49, 50, 51, 52, 53, 54, 63, 72],
46: [1, 10, 19, 27, 28, 29, 36, 37, 38, 45, 47, 48, 49, 50, 51, 52, 53, 55, 64, 73],
47: [2, 11, 20, 27, 28, 29, 36, 37, 38, 45, 46, 48, 49, 50, 51, 52, 53, 56, 65, 74],
48: [3, 12, 21, 30, 31, 32, 39, 40, 41, 45, 46, 47, 49, 50, 51, 52, 53, 57, 66, 75],
49: [4, 13, 22, 30, 31, 32, 39, 40, 41, 45, 46, 47, 48, 50, 51, 52, 53, 58, 67, 76],
50: [5, 14, 23, 30, 31, 32, 39, 40, 41, 45, 46, 47, 48, 49, 51, 52, 53, 59, 68, 77],
51: [6, 15, 24, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 60, 69, 78],
52: [7, 16, 25, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 61, 70, 79],
53: [8, 17, 26, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 62, 71, 80],
54: [0, 9, 18, 27, 36, 45, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 72, 73, 74],
55: [1, 10, 19, 28, 37, 46, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 72, 73, 74],
56: [2, 11, 20, 29, 38, 47, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 72, 73, 74],
57: [3, 12, 21, 30, 39, 48, 54, 55, 56, 58, 59, 60, 61, 62, 66, 67, 68, 75, 76, 77],
58: [4, 13, 22, 31, 40, 49, 54, 55, 56, 57, 59, 60, 61, 62, 66, 67, 68, 75, 76, 77],
59: [5, 14, 23, 32, 41, 50, 54, 55, 56, 57, 58, 60, 61, 62, 66, 67, 68, 75, 76, 77],
60: [6, 15, 24, 33, 42, 51, 54, 55, 56, 57, 58, 59, 61, 62, 69, 70, 71, 78, 79, 80],
61: [7, 16, 25, 34, 43, 52, 54, 55, 56, 57, 58, 59, 60, 62, 69, 70, 71, 78, 79, 80],
62: [8, 17, 26, 35, 44, 53, 54, 55, 56, 57, 58, 59, 60, 61, 69, 70, 71, 78, 79, 80],
63: [0, 9, 18, 27, 36, 45, 54, 55, 56, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74],
64: [1, 10, 19, 28, 37, 46, 54, 55, 56, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74],
65: [2, 11, 20, 29, 38, 47, 54, 55, 56, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74],
66: [3, 12, 21, 30, 39, 48, 57, 58, 59, 63, 64, 65, 67, 68, 69, 70, 71, 75, 76, 77],
67: [4, 13, 22, 31, 40, 49, 57, 58, 59, 63, 64, 65, 66, 68, 69, 70, 71, 75, 76, 77],
68: [5, 14, 23, 32, 41, 50, 57, 58, 59, 63, 64, 65, 66, 67, 69, 70, 71, 75, 76, 77],
69: [6, 15, 24, 33, 42, 51, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 78, 79, 80],
70: [7, 16, 25, 34, 43, 52, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 78, 79, 80],
71: [8, 17, 26, 35, 44, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 78, 79, 80],
72: [0, 9, 18, 27, 36, 45, 54, 55, 56, 63, 64, 65, 73, 74, 75, 76, 77, 78, 79, 80],
73: [1, 10, 19, 28, 37, 46, 54, 55, 56, 63, 64, 65, 72, 74, 75, 76, 77, 78, 79, 80],
74: [2, 11, 20, 29, 38, 47, 54, 55, 56, 63, 64, 65, 72, 73, 75, 76, 77, 78, 79, 80],
75: [3, 12, 21, 30, 39, 48, 57, 58, 59, 66, 67, 68, 72, 73, 74, 76, 77, 78, 79, 80],
76: [4, 13, 22, 31, 40, 49, 57, 58, 59, 66, 67, 68, 72, 73, 74, 75, 77, 78, 79, 80],
77: [5, 14, 23, 32, 41, 50, 57, 58, 59, 66, 67, 68, 72, 73, 74, 75, 76, 78, 79, 80],
78: [6, 15, 24, 33, 42, 51, 60, 61, 62, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 80],
79: [7, 16, 25, 34, 43, 52, 60, 61, 62, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80],
80: [8, 17, 26, 35, 44, 53, 60, 61, 62, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79]
}
BLOCK_INDEX = [20, 23, 47, 53, 77, 80]
# <editor-fold desc="GRID_MASK"
r1 = '111111000'
r2 = '111111000'
r3 = '11.11.000'
# --------------
r4 = '111000111'
r5 = '111000111'
r6 = '11.00011.'
# --------------
r7 = '000111111'
r8 = '000111111'
r9 = '00011.11.'
band_1 = r1 + r2 + r3
band_2 = r4 + r5 + r6
band_3 = r7 + r8 + r9
GRID_MASK = band_1 + band_2 + band_3
# </editor-fold>
GRID_BASE = [
0, 1, 2, 3, 4, 5, 9, 10, 11, 12, 13,
14, 18, 19, 21, 22, 27, 28, 29, 33, 34, 35,
36, 37, 38, 42, 43, 44, 45, 46, 51, 52, 57]
GRID_NEXT = [
6, 7, 8, 15, 16, 17, 20, 23, 24, 25, 26,
30, 31, 32, 39, 40, 41, 47, 48, 49, 50, 53,
54, 55, 56, 63, 64, 65, 72, 73, 74, 77, 80]
GRID_LEFT = [
58, 59, 60, 61, 62,
66, 67, 68, 69, 70,
71, 75, 76, 78, 79]
PAIR_SIZE = len(GRID_BASE)
LEFT_SIZE = len(GRID_LEFT)
CODE_BOOK = [
['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'],
['0', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'],
['0', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'],
['0', 'k', 'm', 'r', 's', 't', 'u', 'w', 'x', 'z']]
DECODE_BOOK = {'.': '00', '0': '00',
'1': '10', '2': '20', '3': '30', '4': '40', '5': '50',
'6': '60', '7': '70', '8': '80', '9': '90',
'A': '11', 'B': '21', 'C': '31', 'D': '41', 'E': '51',
'F': '61', 'G': '71', 'H': '81', 'I': '91',
'a': '12', 'b': '22', 'c': '32', 'd': '42', 'e': '52',
'f': '62', 'g': '72', 'h': '82', 'i': '92',
'k': '13', 'm': '23', 'r': '33', 's': '43', 't': '53',
'u': '63', 'w': '73', 'x': '83', 'z': '93'}
if __name__ == '__main__':
file = __file__
print(f'running {file} ')
else:
file = __file__
print(f'importing {file} ')
- Code: Select all
#!/usr/bin/python3
# <editor-fold desc="Python and Tk version"
"""
Python 3.8.5
Tkinter 8.6
>conda deactivate-(default) => '>' | >conda activate => '(base) >'
"""
# </editor-fold>
# <editor-fold desc="Imports"
import sys
# </editor-fold>
# <editor-fold desc="Imports"
import codec_support as s
import settings as g
# </editor-fold>
# <editor-fold desc="Global Constants"
IS_DEBUG = False
LIST_TYPE = []
PERIOD = '.'
STRING_TYPE = ''
ZERO = '0'
BP = g.BREAK_POINT
DIGITS = g.DIGITS
MAX_CELLS = g.MAX_CELLS
MAX_DIGITS = g.MAX_DIGITS
BLOCK_INDEX = s.BLOCK_INDEX
BLOCK_LIMITED_PEERS = s.BLOCK_LIMITED_PEERS
CODE_BOOK = s.CODE_BOOK
DECODE_BOOK = s.DECODE_BOOK
GRID_BASE = s.GRID_BASE
GRID_MASK = s.GRID_MASK
GRID_LEFT = s.GRID_LEFT
GRID_NEXT = s.GRID_NEXT
LEFT_SIZE = s.LEFT_SIZE
PAIR_SIZE = s.PAIR_SIZE
PEERS = s.PEERS
# </editor-fold>
class Codec():
def __init__(self):
BP
def decode(self, encoded):
'''
:param encodes: 48 char string
encoded with g.CODE_BOOK
(strings are converted to list)
members of value in g.VALID_GRID_ENTRIES
:return: Sudoku 81-char string
'''
try:
decode_grid = ['0'] * MAX_CELLS
given_grid = ['0'] * MAX_CELLS
solved_grid = ['0'] * MAX_CELLS
j = 0
for i, x in enumerate(GRID_MASK):
if x == '1':
value = encoded[j]
result = DECODE_BOOK[value]
j += 1
else:
result = '00'
decode_grid[i] = result
for i, (digit, code_index) in enumerate(decode_grid):
solved_grid[i] = digit
if IS_DEBUG:
u.print_grid(decode_grid, 'decode_grid')
u.print_grid(solved_grid, 'solved_grid')
# <editor-fold desc="Solve solved_grid for full house in its blocks"
for index in BLOCK_INDEX:
peers = BLOCK_LIMITED_PEERS[index]
digits = DIGITS
for digit_index in peers:
digit = solved_grid[digit_index]
if digit in digits:
digits = digits.replace(digit, '')
if len(digits) == 1:
solved_grid[index] = digits
break
if IS_DEBUG:
u.print_grid(solved_grid, 'solved_grid')
BP
# </editor-fold>
# <editor-fold desc="Solves remainder of solved_grid"
for i, digit in enumerate(solved_grid):
if digit == '0':
peers = PEERS[i]
digits = DIGITS
for digit_index in peers:
digit = solved_grid[digit_index]
if digit in digits:
digits = digits.replace(digit, '')
if len(digits) == 1:
solved_grid[i] = digits
break
if IS_DEBUG:
u.print_grid(solved_grid, 'solved_grid')
BP
# </editor-fold>
# <editor-fold desc="Solves given_grid"
given_grid = solved_grid.copy()
write_base = {'0': False, '1': False, '2': True, '3': True}
write_next = {'0': False, '1': True, '2': False, '3': True}
for i in range(PAIR_SIZE):
base_index = GRID_BASE[i]
next_index = GRID_NEXT[i]
(digit, code_index) = decode_grid[base_index]
if write_base[code_index]:
given_grid[base_index] = PERIOD
if write_next[code_index]:
given_grid[next_index] = PERIOD
BP
for i in range(LEFT_SIZE):
base_index = GRID_LEFT[i]
(digit, code_index) = decode_grid[base_index]
if code_index == '1':
given_grid[base_index] = PERIOD
if IS_DEBUG:
u.print_grid(given_grid, 'given_grid')
BP
# </editor-fold>
given = ''.join(given_grid)
solved = ''.join((solved_grid))
return (given, solved)
except Exception as e:
print(e)
print('in codec.encode_puz')
sys.exit()
#
def encode(self, given, solved):
try:
assert len(given) == MAX_CELLS
assert len(solved) == MAX_CELLS
assert type(given) == type(STRING_TYPE)
assert type(solved) == type(STRING_TYPE)
# todo assert members are in g.VALID_GRID_ENTRIES
encoded = ''
given_mask = [ZERO] * MAX_CELLS
given = given.replace(PERIOD, ZERO)
given_grid = list(given)
solved_grid = list(solved)
for i in range(len(given_grid)):
if given_grid[i] > ZERO:
given_mask[i] = '1'
cd = {'00': 3, '01': 2, '10': 1, '11': 0}
for i in range(PAIR_SIZE):
base_index = GRID_BASE[i]
next_index = GRID_NEXT[i]
dig_idx = int(solved_grid[base_index])
c1 = given_mask[base_index]
c2 = given_mask[next_index]
code = CODE_BOOK[cd[c1 + c2]][dig_idx]
encoded += code
BP
for i in range(LEFT_SIZE):
index = GRID_LEFT[i]
dig_idx = int(solved_grid[index])
c2 = given_mask[index]
code = CODE_BOOK[cd['1' + c2]][dig_idx]
encoded += code
BP
return encoded
except Exception as e:
print(e)
print('in codec.encode_puz')
sys.exit()
#
if __name__ == '__main__':
file = __file__
print(f'running {file} ')
# <editor-fold desc="Given Grid"
r1 = '.8..749.5'
r2 = '..9.382.4'
r3 = '4...9268.'
# --------------
r4 = '..74.58..'
r5 = '84.917.6.'
r6 = '..18.34..'
# --------------
r7 = '..83417.6'
r8 = '736259148'
r9 = '1.4786.9.'
band_1 = r1 + r2 + r3
band_2 = r4 + r5 + r6
band_3 = r7 + r8 + r9
original_given = band_1 + band_2 + band_3
# </editor-fold>
# <editor-fold desc="Solved Grid"
r1 = '682174935'
r2 = '519638274'
r3 = '473592681'
# --------------
r4 = '367425819'
r5 = '845917362'
r6 = '291863457'
# --------------
r7 = '958341726'
r8 = '736259148'
r9 = '124786593'
band_1 = r1 + r2 + r3
band_2 = r4 + r5 + r6
band_3 = r7 + r8 + r9
original_solved = band_1 + band_2 + band_3
# </editor-fold>
sdk = Codec()
sudoku_encoded = sdk.encode(original_given, original_solved)
sudoku_decoded = sdk.decode(sudoku_encoded)
decoded_given = sudoku_decoded[0]
decoded_solved = sudoku_decoded[1]
BP
else:
file = __file__
print(f'importing {file} ')
# <editor-fold desc="How the cell pairing works"
'''
The following applies to the decode_grid list whose members are two digits
in string format.
1. Digit One = cell value (in range 0,1,2,3,4,5,6,7,8,9) 0 = not solved
2. Digit Two = index to the code/decode alphabet (in range 0, 1, 2, 3)
There are 33 cells which are removed in the 'encoded' sudoku string, leaving
48 'base' cells. The first 33 of these 'base' cells are paired with one
of the 33 'next' (removed cells) to describe their paired status. This
is described by CODE_BOOK with four possible encryption alphabets.
These paired cells are indexed in the following two list of length 33:
Codec.Grid_base = index of base cell of a pair
Codec.Grid_next = index of next cell of a pair
If a cell is not indexed in the Code.Grid_base list than it is one of the 48
cells not paired with one of the 33 'next' cells. Therefore the "Digit Two"
previously described, is indexed in the list "CLUE_TYPE" as either a 1 or 2.
The 1 meaning a GIVEN cell or a SOLVED cell.
However, if the index of those first 33 'base' cells to be in the 'encoded' string
is found in Codec.Grid_base then is has an index to its corresponding 'next' cell
which is found in Codec.Grid_next at the same index value in both lists.
The afore mentioned "Digit Two" now has four possible encrypted alphabets shown
in the PAIR_TYPE list below.
Cell Pairs
Visible-Invisible or base-next
-----------------
0 = G-G Given-Given
1 = G-S Given-Solve
2 = S-G Solve-Given
3 = S-S Solve-Solve
'''
# </editor-fold>
