• # Ancient Hindu Problems

Dr Yossi Elran explains what Ancient Hindu problems are and how to solve them
© Davidson Institute of Science Education, the educational arm of the Weizmann Institute of Science

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Hindu problems originated in India in the middle ages and are sometimes referred to as arithmetical restorations or skeleton problems. In these problems, digits are replaced by asterisks, for example: * + * = 2.
Each asterisk represented one missing digit (from 0 and 9). Two or more asterisks in the same problem may represent different digits.
For example, for the problem * + * = 2 there are two possible solutions:
• 1 + 1 = 2 – in this solution each asterisk represents the digit 1
• 2 + 0 = 2 – in this solution one asterisk represents the digit 0 and the other asterisk represents the digit 2
Note that we are counting 2 + 0 and 0 + 2 as the same solution.
Remember the following points:
• Some puzzles might have several solutions and some might have no solution
• Two adjacent asterisks represent a 2-digit number, like 74. Three adjacent asterisks represent a 3-digit number, and so on. In these cases the leftmost asterisk cannot represent the number 0, i.e. it is illegal to write to represent the number 8 as 08.
In the next step you will see a slideshow of some basic Hindu cryptarithms
© Davidson Institute of Science Education, the educational arm of the Weizmann Institute of Science

#### Maths Puzzles: Cryptarithms, Symbologies and Secret Codes  