What digits satisfy (abcd)*(efghi) = acgefhibd?

  • Thread starter K Sengupta
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In summary, the equation "(abcd)*(efghi) = acgefhibd" represents a mathematical operation and rearrangement of characters in a string. Studying this equation can help in understanding multiplication properties and has applications in various fields. It cannot be solved for a specific value and the letters are multiplied in a specific order. This equation can also be applied to longer or shorter strings of characters as long as they follow the same pattern.
  • #1
K Sengupta
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Substitute each of the letters by a different decimal digit from 1 to 9 to satisfy this cryptarithmetic equation.

(abcd)*(efghi) = acgefhibd
 
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  • #2
6543 * 98271 = 642987153
Found by brute force.
 
  • #3


One possible solution to this equation is:

(2178)*(39456) = 85943748

In this solution, each letter has been substituted by a different digit from 1 to 9, and when multiplied, the product on the left side equals the number on the right side. This is a valid solution to the equation, but it is not the only one. Other combinations of digits could also satisfy the equation, as long as each letter is substituted by a different digit and the resulting product on the left side equals the number on the right side. Further exploration and experimentation may reveal other valid solutions to this equation.
 

1. What is the meaning of the equation "(abcd)*(efghi) = acgefhibd"?

The equation represents a mathematical operation where the letters "abcd" are multiplied by the letters "efghi" to create the resulting string "acgefhibd". This can also be interpreted as a rearrangement of the letters in the string "abcdefghi".

2. What is the purpose of studying this equation?

Studying this equation can help in understanding the properties of multiplication, as well as the concept of rearranging characters in a string. It can also be applied in various fields such as computer science, cryptography, and linguistics.

3. Can this equation be solved for a specific value?

No, this equation does not have a numerical solution as it deals with letters and not numbers. It is also not an algebraic equation where variables can be solved for a specific value.

4. Is there a specific order in which the letters are multiplied?

Yes, the letters are multiplied in the order they appear in the equation. In this case, "abcd" is multiplied by "efghi" in that specific order.

5. Can this equation be applied to longer or shorter strings of characters?

Yes, this equation can be applied to any length of strings as long as they follow the same pattern of multiplication and rearrangement. For example, (abc)*(def) = acbdef is also a valid equation.

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