Who's name is hidden in here?

Who's name is hidden in here?

Show answer

Answer: MENDELEEV¹

The circles in the puzzle are arranged in a $$26 \times 26$$ grid with 26 rows and 26 columns. If we identify the rows of the grid from top to bottom with successive uppercase letters and the columns from left to right with successive lowercase letters, then the position of each circle in the grid can be represented by two letters: the uppercase letter that identifies the row of the circle, followed by the lowercase letter that identifies its column. However, the position of a circle on the main diagonal is represented by a single letter: the uppercase letter that identifies the row (and thus also corresponds to the letter that identifies the column).

This is how the puzzle can be solved. Circles at positions that correspond to a the symbolic representation of a chemical elements from the periodic table are indicated in red. These circles must be ignored: only the other circles are important to find the answer and are indicated in green. The green circles are numbered sequentially from 1 by the digits in those circles (indicated in the small black circles near the green circles). This determines the order in which the representations of the positions of the green circles must be concatenated: the green circle with digit 1 is at position M, the green circle with digit 2 at position En, the green circle with digit 3 at position De, the green circle with digit 4 at position Le and the green circle with digit 5 at position Ev. Concatenating the representations of these positions yields the name MENDELEEV.

If you now take a closer look, you'll see that the red circles correspond to positions represented by one or two letters of symbols for chemical elements from the periodic table²: a systematic arrangement of all known chemical elements. These red circles must be ignored: only the green circles are important to find the answer.

Taking a look at what numbers are in the five green circles in the original puzzle (we have put them inside small black circles near the green circles), you'll see that the green circles are numbered sequentially, starting from 1. This determines the order in which the representations of the positions of the green circles must be concatenated: the green circle with number 1 is at position M, the green circle with number 2 at position En, the green circle with number 3 at position De, the green circle with number 4 at position Le and the green circle with number 5 at position Ev. Concatenating the representations of these positions yields the name MENDELEEV.

Assignment

A puzzle file is a text file with 26 lines, each containing 26 digits (0–9). For example, this is the puzzle file corresponding to the puzzle from the introduction (puzzle.txt³):

00300080000450000528300000
37001006505000000500000000
60238400000773300910400000
07003000000000000020000010
00000000000002000540550000
00006200000290000700000000
70033000000000000000000000
00006526000000100040000000
00000000200006000800000000
00000000000000000000000000
00000000002000000100000000
50004000500000000600290000
00990070000019600003000000
42079006700001760000000000
00000010000000100060000000
57070000000030350808100000
00000000000000000000000000
45008316000002000000800000
04408080900026000470000000
21803001400380000040000000
00000000000000000000600000
00000000000000000000070000
00000000000000000000001000
00003000000000000000000000
07000000000000000000000040
00000000000004000300000000

Each zero (digit 0) in this file corresponds to a position where there is no circle in the puzzle and each other digit corresponds to a position where there is a black circle in the puzzle containing that digit. A puzzle file therefore corresponds to a representation of the puzzle where we would also draw circles containing a zero at positions where there are zeros in the file.

Representation of the puzzle from the introduction, where grey circles containing a zero (digit 0) have been drawn at positions where there is a zero in the puzzle file. The rows of the puzzle grid have been numbered from top to bottom and the columns have been numbered from left to right, starting at zero.

In the above representation of the puzzle we have numbered the rows from top to bottom, starting at zero. We have also numbered the columns from left to right, starting at zero. This allows us to represent any position in the $$26 \times 26$$ puzzle grid as a coordinate: a tuple $$(r, c)$$ with two integers $$r, c \in \mathbb{N}$$ (int; $$0 \leq r, c < 26$$). By identifying the rows and columns with letters as in the introduction, we can also represent each position in the puzzle grid symbolically as a single letter (str; for positions on the main diagonal) or two letters (str; for positions off the main diagonal).

Your task:

Write a function symbol2coordinate that takes the symbolic representation (str) of a position $$p$$ in the $$26 \times 26$$ puzzle grid. The function must return the coordinate (tuple) of position $$p$$. No distinction should be made between uppercase and lowercase letters when interpreting the symbolic representation of the position.
Write a function coordinate2symbol that takes the coordinate (tuple) of a position $$p$$ in the $$26 \times 26$$ puzzle grid. The function must return the symbolic representation (str; in uppercase) of position $$p$$.
Write a function symbols that takes two arguments: i) the location (str) of a CSV file⁴ with UTF-8⁵ character encoding and ii) the number $$i$$ (int) of a field (column) in the CSV file. The first line in the CSV file contains a header. The fields of a CSV file are numbered sequentially starting from 1 and are separated by commas (,). A field that itself contains commas must be enclosed in double quotes ("). Other fields may optionally be enclosed in double quotes. The function must return a set containing the content (str) of the $$i$$-th field of all CSV records from the file (without the header) where this field consists of one or two letters. In addition, that content must be converted to uppercase, and the content must be reduced to a single letter if it consists of two of the same letters (for example, xx must be converted to X).

Tip

Use the csv module⁶ to process records of CSV files.
Write a function all_coordinates that takes the location (str) of a puzzle file. The function must return a dictionary (dict) that maps each coordinate (tuple) of a circle in the puzzle grid onto the digit (int) in that circle.
Write a function valid_coordinates that takes two arguments: i) the location (str) of a puzzle file and ii) a collection (list, tuple or set) containing the symbolic representation (str) of all invalid positions in the puzzle grid. The function must return a dictionary (dict) that maps each coordinate (tuple) of a circle in the puzzle grid that is not at an invalid position onto the digit (int) in that circle.
Write a function hidden_name that takes two arguments: i) the location (str) of a puzzle file and ii) a collection (list, tuple or set) containing the symbolic representation (str) of all invalid positions in the puzzle grid. The function must return the name (str; in uppercase) hidden in the puzzle.

Solution

In the following interactive session we assume that the text files symbols.csv⁷ and puzzle.txt⁸ are located in the current directory.

        >>> symbol2coordinate('Ac')
(0, 2)
>>> symbol2coordinate('B')
(1, 1)
>>> symbol2coordinate('MG')
(12, 6)

>>> coordinate2symbol((0, 2))
'AC'
>>> coordinate2symbol((1, 1))
'B'
>>> coordinate2symbol((12, 6))
'MG'

>>> invalid_symbols = symbols('symbols.csv9', 2)
>>> invalid_symbols
{'AC', 'AG', 'AL', 'AM', 'AR', 'AS', 'AT', 'AU', 'B', 'BA', 'BE', 'BH', 'BI', 'BK', 'BR', 'C', 'CA', 'CD', 'CE', 'CF', 'CL', 'CM', 'CN', 'CO', 'CR', 'CS', 'CU', 'DB', 'DS', 'DY', 'ER', 'ES', 'EU', 'F', 'FE', 'FL', 'FM', 'FR', 'GA', 'GD', 'GE', 'H', 'HE', 'HF', 'HG', 'HO', 'HS', 'I', 'IN', 'IR', 'K', 'KR', 'LA', 'LI', 'LR', 'LU', 'LV', 'MC', 'MD', 'MG', 'MN', 'MO', 'MT', 'N', 'NA', 'NB', 'ND', 'NE', 'NH', 'NI', 'NO', 'NP', 'O', 'OG', 'OS', 'P', 'PA', 'PB', 'PD', 'PM', 'PO', 'PR', 'PT', 'PU', 'RA', 'RB', 'RE', 'RF', 'RG', 'RH', 'RN', 'RU', 'S', 'SB', 'SC', 'SE', 'SG', 'SI', 'SM', 'SN', 'SR', 'TA', 'TB', 'TC', 'TE', 'TH', 'TI', 'TL', 'TM', 'TS', 'U', 'V', 'W', 'XE', 'Y', 'YB', 'ZN', 'ZR'}

>>> all_coordinates('puzzle.txt10')
{(0, 2): 3, (0, 6): 8, (0, 11): 4, (0, 12): 5, (0, 17): 5, (0, 18): 2, (0, 19): 8, (0, 20): 3, (1, 0): 3, (1, 1): 7, (1, 4): 1, (1, 7): 6, (1, 8): 5, (1, 10): 5, (1, 17): 5, (2, 0): 6, (2, 2): 2, (2, 3): 3, (2, 4): 8, (2, 5): 4, (2, 11): 7, (2, 12): 7, (2, 13): 3, (2, 14): 3, (2, 17): 9, (2, 18): 1, (2, 20): 4, (3, 1): 7, (3, 4): 3, (3, 18): 2, (3, 24): 1, (4, 13): 2, (4, 17): 5, (4, 18): 4, (4, 20): 5, (4, 21): 5, (5, 4): 6, (5, 5): 2, (5, 11): 2, (5, 12): 9, (5, 17): 7, (6, 0): 7, (6, 3): 3, (6, 4): 3, (7, 4): 6, (7, 5): 5, (7, 6): 2, (7, 7): 6, (7, 14): 1, (7, 18): 4, (8, 8): 2, (8, 13): 6, (8, 17): 8, (10, 10): 2, (10, 17): 1, (11, 0): 5, (11, 4): 4, (11, 8): 5, (11, 17): 6, (11, 20): 2, (11, 21): 9, (12, 2): 9, (12, 3): 9, (12, 6): 7, (12, 12): 1, (12, 13): 9, (12, 14): 6, (12, 19): 3, (13, 0): 4, (13, 1): 2, (13, 3): 7, (13, 4): 9, (13, 7): 6, (13, 8): 7, (13, 13): 1, (13, 14): 7, (13, 15): 6, (14, 6): 1, (14, 14): 1, (14, 18): 6, (15, 0): 5, (15, 1): 7, (15, 3): 7, (15, 12): 3, (15, 14): 3, (15, 15): 5, (15, 17): 8, (15, 19): 8, (15, 20): 1, (17, 0): 4, (17, 1): 5, (17, 4): 8, (17, 5): 3, (17, 6): 1, (17, 7): 6, (17, 13): 2, (17, 20): 8, (18, 1): 4, (18, 2): 4, (18, 4): 8, (18, 6): 8, (18, 8): 9, (18, 12): 2, (18, 13): 6, (18, 17): 4, (18, 18): 7, (19, 0): 2, (19, 1): 1, (19, 2): 8, (19, 4): 3, (19, 7): 1, (19, 8): 4, (19, 11): 3, (19, 12): 8, (19, 18): 4, (20, 20): 6, (21, 21): 7, (22, 22): 1, (23, 4): 3, (24, 1): 7, (24, 24): 4, (25, 13): 4, (25, 17): 3}

>>> valid_coordinates('puzzle.txt11', invalid_symbols)
{(3, 4): 3, (4, 13): 2, (4, 21): 5, (11, 4): 4, (12, 12): 1}

>>> hidden_name('puzzle.txt12', invalid_symbols)
'MENDELEEV'