Cryptarithms are mathematical puzzles, where numbers are replaced by letters or symbols. Each letter represents a unique digit, and the challenge is to decode the puzzle using logical reasoning and arithmetic skills. Cryptarithms is also called as alphametics.
Each letter stands for one number from \(0\) to \(9\). The goal is to find which digit each letter represents.
How to Solve Digits in Disguise?
- Remember each letter is one number, always the same number wherever it appears.
- Different letters stand for different numbers.
- Use simple math rules to guess which numbers fit.
- Check if the sum or product is right after you guess.
Example:
1.
Here, a single digit \(T\) is added \(3\) times, and it turns into a two-digit number \(UT\). That is, the unit digit of the resultant is again the same number \((T)\).
It is only possible when \(T\) is \(5\).
\(5 + 5 + 5 = 15\)
Therefore, \(UT\) is \(15\).
2.
Here, the unit digit \(2 + 2 = 4\). Thus, \(K = 4\).
The sum becomes .
Tens Column: \(S + S = A4\). Since \(S\) is a single digit, the maximum sum \(S + S\) is \(18\). Thus, the hundreds digit \(A\) must be \(1\).
\(S + S = 14 \implies 2S = 14 \implies S = 7\).
Therefore, we have \(72 + 72 = 144\).
Hence, \(S = 7\), \(A = 1\) and \(K = 4\).