Tips And Tricks And Shortcuts To Solve Cryptarithmetic Questions
Tips and Tricks and Shortcuts to Solve Cryptarthmetic Questions
As mentioned in the introduction page Cryptarithmetic is considered to be, both a science as well as an art.
Hence apart from logic, one must use his/her presence of mind and a little bit of common sense to solve the problems.
Below mentioned are some thumb rules and principles that need to be followed while solving Cryptarithmetics questions, some of which are mentioned below:
Rules to remember:
1. Assigning digits to each letter or alphabet:
Under this each letter will be assigned a particular digit, and if the same letter is being used again in the word than, it will be denoted with the same digit which is allotted to it.
2. Each letter has its own unique value:
Just like we are assigned an individual Roll number in a class, similarly, while solving such questions each letter will be assigned its own unique value, making it clear that no two letter can have the same digit or a number or a value.
For example: If a digit 4 is allotted to alphabet F, then this number cannot be assigned to any other alphabet.
The digit assigned to the letter will remain the same throughout the question.
The digits assigned must have a numerical base ranging from 0 to 9
The resultant numbers should not begin with 0.
3. Cross-checking or Checking of Errors:
Now after doing all the algorithm and finding out the digits assigned to each letter, we need to cross verify the resultant, which means we must put the digits in place of the corresponding letters and the resulting arithmetic operations must be correct.
For doing this there are certain pre requisites which need to be considered which are mentioned below:
1. The total number of letters must not be more than 10.
2. The length of the answer should match with the operand.
3. In case the length of the answer does not match, then must not exceed more than. Simply put the answer must be only one more than the operand.
Below mentioned is an example supporting the above tips and tricks, for better understanding of the students:
Decode and solve the below mentioned CryptArithmetic problem:
Here the resultant is 1 more than operand, which makes it clear that the sum of the digits denoting S and M is greater than 10.
“M” can only equal 1 because it is the “carry 1” from the column S+M=O (+10). In other words, every time addition of “n” digits gives a total of “n+1” digits, the left-hand digit of the total must be “1”.
A blind search can eventually find the solutions, if there is any, in a bound time. Given that the base of the number is 10, there may be 10 solutions to be checked in the problem space; where n is the number of unique letters or symbols in the problem. A rule based searching technique can provide the solution in minimum time.
When constraints are applied to the problem if there are any, the solution space to be searched decreases.