1. PROJECT OF MATHEMATICS SUBMITTED TO MR.SUNIL MITTAL SUBMITTED BY- BHAVISHYA SINGLA CLASS- XTH-A ROLL NO.4

2. BIBLIOGRAPHY INTERNET- www.google.com www.cryptarithms.com www.futurelearn.com www.merriam-webster.com brainly.in mathworld.wolfram.com www.puzzles-to-print.com

3. CRYPTARITHM BY BHAVISHYA SINGLA

4. MEANING OF CRYPTARITHM  Cryptarithm, mathematical recreation in which the goal is to decipher an arithmetic problem in which letters have been substituted for numerical digits.

5. VARIOUS FAQ’S ABOUT CRYPTARITHM  What are the uses of Cryptarithm- Cryptarithm now denotes mathematical problems usually calling for addition, subtraction, multiplication, or division and replacement of the digits by letters of the alphabet or some other symbols.  What are the various types of Cryptarithm- Types of cryptarithm include the alphametic, the digimetic, and the skeletal division.  What is Cryptarithmetic problem- Cryptarithmetic problems are mathematical puzzles in which the digits are replaced by letters of the alphabets. Cryptarithmetic questions are most commonly asked in the Infosys recruitment and eLitmus exam. Solving a Cryptarithmetic Problem will take nearly 10-12 minutes in exam  What is meant by Cryptarithm- an arithmetic problem in which letters have been substituted for numbers and which is solved by finding all possible pairings of digits with letters that produce a numerically correct answer.

6. VARIOUS FAQ’S ABOUT CRYPTARITHM  Who invented Cryptarithm- One of the most famous was invented by Henry Ernest Dudeney, a British puzzlist, in 1924: SEND + MORE = MONEY.  What is Cryptarithmetic problem in AI- Cryptarithmetic Problem is a type of constraint satisfaction problem where the game is about digits and its unique replacement either with alphabets or other symbols. In cryptarithmetic problem, the digits (0-9) get substituted by some possible alphabets or symbols.

7. VARIOUS TYPES OF CRYPTARITHM AlphameticDigimeticSkeletal division

8. RULES TO SOLVE CRYPTARITHM Just as in a cryptogram, each different letter corresponds to a different number and all instances of a particular letter corresponds to a particular number. RULE 1 There should be only one possible solution to each cryptarithm. RULE 2 The left most digit in each line is never a zero RULE 3

9. ALPHAMETIC CRYPTARITHM  Alphametics are cryptarithms that spell out words. Given a mathematical expression, every digit in the expression is replaced by a letter. One of the most famous alphametics, spelling out ‘SEND MORE MONEY’ appears above. This alphametic was first published by Henry Dudeney, a British puzzlist, in 1924. 1.Five rules govern alphametics:Identical digits are replaced by the same letter. Different digits are replaced by different letters. 2.After replacing all the letters with digits, the resulting arithmetic expression must be mathematically correct. 3.Numbers cannot start with 0. For example, the number 0900 is illegal. 4.Each problem must have exactly one solution, unless stated otherwise (unlike the “Hindu” problems where there might be no solution or multiple solutions). 5.The problems will be in base 10 unless otherwise specified. This means that the letters replace some or all of the 10 digits – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.  Alphametics are cryptarithms that spell out words. Given a mathematical expression, every digit in the expression is replaced by a letter. One of the most famous alphametics, spelling out ‘SEND MORE MONEY’ appears above. This alphametic was first published by Henry Dudeney, a British puzzlist, in 1924.

10. EXAMPLES OF ALPHAMETIC CRYPTARITHM

11. DIGIMETIC CRYPTARITHM  Cryptarithms are number puzzles in which a group of arithmetical operations has some or all of its digits replaced by letters or symbols, and where the original digits must be found. Digimetic cryptarithms are ones in which numbers are substituted for other numbers.

12. EXAMPLES OF DIGIMETIC CRYPTARITHM

13. SKELETAL DIVISION CRYPTARITHM  A long division in which most or all of the digits are replaced by symbols (usually asterisks) to form a cryptarithm. Cryptarithms are a type of mathematical puzzle in which the digits are replaced by symbols. Normally alphabets are used

14. EXAMPLES OF SKELETAL DIVISION CRYPTARITHM

15. ACKNOWLEGMENT  I AM REALLY THANKFULL TO RESPECTED PRINCIPLE, VICE PRINCIPLE, STUDENTS OF CLASS 10 TH -A AND I ALSO THANKS TO MY MATH TEACHER FOR GIVING ME GUIDANCE AND GUIDANCE TO COMPLETE MY MATH PROJECT. I AM ALSO THANKFULL TO DEVELOPERS WHOSE WEBSITE HELPS ME TO FULLFILL MY PROJECT WORK.