Puzzles and Rebuses, Reconstruct the Exercise / Cryptarithmetic

Cryptarithmetic puzzles (or cryptarithms) are arithmetic problems where digits are replaced by letters. The goal is to assign a unique digit (0-9) to each letter to make the arithmetic operation (like addition, subtraction, multiplication) mathematically correct. These require logic and number sense.

• A mistake in the exercise

  Prove that there is an error in the following multiplication problem:

  \(\begin{array}& & & * & * & * & 2 & 7 \\ \times & & & & & * & * \\ \hline & * & * & * & * & * & 6 \\ + & * & * & * & * & * & \\ \hline & * & * & * & * & 4 & 6 \end{array}\)

  Topics:

  Arithmetic Logic -> Reasoning / Logic Proof and Example -> Proof by Contradiction Number Theory -> Division Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Beno Arbel Olympiad, 2013, Grade 7 Question 4

• Question

  In the following arithmetic puzzle, different digits have been replaced by different letters, and identical digits – by identical letters. Reconstruct the puzzle:

  `BAOxxBAxxB=2002`

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Inequalities Logic -> Reasoning / Logic Number Theory -> Prime Numbers -> Prime Factorization Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic

• Reconstruct the Exercise

  Reconstruct the digits in the following exercise:

  

  Topics:

  Arithmetic Number Theory -> Division Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic

• Baobab

  In the following exercise, identical digits have been replaced with identical letters, and different digits have been replaced with different letters. Reconstruct the exercise.

  `BAOxxBAxxB = 2002`

   

   

   

   

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Logic -> Reasoning / Logic Number Theory -> Prime Numbers -> Prime Factorization Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic

• Letter Replacement

  Each letter represents a different digit; whenever a specific letter appears, it is necessarily the same digit.

  Find `B-E/2`

  Given: `AB*C=DE`

  And also `F^D=GF`

  Show hint

  Log in here to receive the hint
  Topics:

  Number Theory -> Prime Numbers Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Number Theory -> Division Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic

• ABC

  In the following exercise, different digits have been replaced with different letters, and identical digits have been replaced with identical digits. Find the three-digit number ABC

  `ABC - A -B-C=DCA`

  Topics:

  Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 2

• SLV LVS BLS

  In the following expression, different letters represent different digits, and identical letters represent identical digits:

  SLV = LVS + BLS

  Find the number SLV.

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rule by 11 Algebra -> Equations Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 3

• Question

  In the following addition problem, different shapes replace different digits, and identical shapes replace identical digits:

  `triangle square triangle square triangle+ square triangle square triangle square = o+ triangle triangle triangle triangle o+`

  What is the result of the addition?

  Topics:

  Arithmetic Algebra -> Equations Logic -> Reasoning / Logic Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 3

• The Disguised Digits

  In the following division exercise, (almost) all the digits are disguised!

  What is the dividend?

  \(\begin{align*} &\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }**\text{ }8**\\ &\overline{* * * * * * *\text{ } *}| * *\text{ } *\\ &\underline{\text{ }\text{ }* *\text{ } *}\\ &\text{ }\text{ }\text{ }\text{ }\text{ }* * * *\\ &\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\underline{\text{ }\text{ }* *\text{ } *}\\ &\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }* * * *\\ &\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\underline{* * *\text{ } *}\\ \end{align*}\)

  Topics:

  Arithmetic Number Theory -> Division Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Bar-Ilan's weekly mathriddle competition, 2024 Question 8

• Question

  In this letter exercise, identical letters represent identical digits, different letters represent different digits, and asterisks represent any digit. Find all the digits.
  `(ABCD)^2 = A B ** ** ** C D `

  Topics:

  Number Theory Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Beno Arbel Olympiad, 2017, Grade 8 Question 4