Cryptarithm Puzzle Techniques

Cryptarithm

Solving Techniques

• Definition: A puzzle where the digits are replaced by letters or symbols, and the goal is to find the original digits.

• Basic Rules:

  • Each letter represents a different digit (0-9).
  • A letter cannot represent more than one digit.
  • Numerical constraints (e.g., first digit can't be zero in a multi-digit number).

• Common Techniques:

  1. Substitution: Start substituting letters with digits systematically.
  2. Trial and Error: Test combinations to find valid solutions.
  3. Backtracking: Recursively try combinations and backtrack if an invalid state is reached.
  4. Logical Deduction: Use the properties of arithmetic to derive possible values (e.g., sum constraints).
  5. Digit Analysis: Assess the maximum and minimum values for combinations, often starting from the leftmost (most significant) digits.

Examples

1. Example 1: SEND + MORE = MONEY

   • Setup: Assign each letter a digit.
   • Key Solutions:
     • S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2.
     • Equation holds: 9567 + 1085 = 10652.

2. Example 2: BASE + BALL = GAMES

   • Setup: Similar to SEND + MORE.
   • Key Solutions:
     • B = 1, A = 0, S = 9, E = 5, L = 7, G = 2, M = 6.
     • Equation holds: 1095 + 1077 = 2172.

Practice Problems

1. Problem 1: CROSS + ROADS = DANGER

   • Try to assign digits to letters C, R, O, S, A, D, N, G, E.

2. Problem 2: 2 * SEND = MORE

   • Find digits for S, E, N, D, M, O, R.

3. Problem 3: MEET + MEET = TREAT

   • Determine digits for M, E, T, R, A.

4. Problem 4: FLIP + FLAP = FLICK

   • Assign values to F, L, I, P, A, C, K.

5. Problem 5: A + B = C

   • Where A, B, C are single-digit numbers. Explore combinations under the constraint of no leading zeros.

Cryptarithm

• A puzzle where letters or symbols replace digits, the goal is to decipher the original digits.
• Each letter represents a unique digit from 0 to 9.
• A letter can't represent multiple digits.
• The first digit of a multi-digit number can't be zero.
• Common techniques include substitution, trial and error, backtracking, logical deduction, and digit analysis.

Solving Techniques

• Substitution: Start by systematically assigning digits to letters.
• Trial and Error: Test different combinations to find solutions.
• Backtracking: Recursively explore combinations, backtracking if an invalid state is reached.
• Logical Deduction: Use arithmetic properties to narrow down possible values (e.g., sum constraints).
• Digit Analysis: Analyze the maximum and minimum values for combinations, often starting from the leftmost (most significant) digits.

Examples

SEND + MORE = MONEY

• Solution: S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2
• Equation: 9567 + 1085 = 10652

BASE + BALL = GAMES

• Solution: B = 1, A = 0, S = 9, E = 5, L = 7, G = 2, M = 6
• Equation: 1095 + 1077 = 2172

Practice Problems

• CROSS + ROADS = DANGER: Assign digits to letters C, R, O, S, A, D, N, G, E.
• 2 * SEND = MORE: Find digits for S, E, N, D, M, O, R.
• MEET + MEET = TREAT: Determine digits for M, E, T, R, A.
• FLIP + FLAP = FLICK: Assign values to F, L, I, P, A, C, K.
• A + B = C: Where A, B, C are single-digit numbers. Explore combinations with no leading zeros.