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 courses:be5b33prg:homeworks:character_equations [2016/01/25 09:34]xposik created courses:be5b33prg:homeworks:character_equations [2016/01/25 09:37]xposik [Introduction] 2016/01/25 09:41 xposik [Evaluation] 2016/01/25 09:37 xposik [Introduction] 2016/01/25 09:34 xposik created 2016/01/25 09:41 xposik [Evaluation] 2016/01/25 09:37 xposik [Introduction] 2016/01/25 09:34 xposik created Last revision Both sides next revision Line 15: Line 15: which is a correct mathematical equation. It is also a Python expression which evaluates to ''​True''​. which is a correct mathematical equation. It is also a Python expression which evaluates to ''​True''​. - - **Further requirements for valid solutions:​** - - - The solution is a mutually unique assignement of digits and letters. The same letters always represent the same digits, different letters must represent different digits. E.g. if you decide that letter ''​P''​ represents digit ''​6'',​ you have to substitute this digit for all the ''​P''​s in the equation, and also no other letter can represent digit ''​6''​. - - The first letters of all "​words"​ (including single-character "​words"​) cannot represent digit 0, since we usually do not write the initial zeros. Another example of character equation may be the following puzzle and its solution: Another example of character equation may be the following puzzle and its solution: Line 25: Line 20: (J + O + I + N + T)**3 == JOINT (J + O + I + N + T)**3 == JOINT (1 + 9 + 6 + 8 + 3)**3 == 19683 (1 + 9 + 6 + 8 + 3)**3 == 19683 + + **Further requirements for valid solutions:​** + + - The solution is a mutually unique assignement of digits and letters. The same letters always represent the same digits, different letters must represent different digits. E.g. if you decide that letter ''​P''​ represents digit ''​6'',​ you have to substitute this digit for all the ''​P''​s in the equation, and also no other letter can represent digit ''​6''​. + - The first letters of all "​words"​ (including single-character "​words"​) cannot represent digit 0, since we usually do not write the initial zeros. (In the first example above, neither ''​A'',​ nor ''​B''​ can be 0. In the second example, no character can be zero, since all are part of single-character words.) Published character equations usually have only a single solution. In general (and in this task in particular),​ this feature is not always fulfilled. We would like to find all possible solutions. Published character equations usually have only a single solution. In general (and in this task in particular),​ this feature is not always fulfilled. We would like to find all possible solutions.