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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
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
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Maths Puzzles: Cryptarithms, Symbologies and Secret Codes

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