Solve ABCADE Cryptarithmetic Puzzle - Square BAE

[K Sengupta]

Substitute each of the letters A, B, C, D and E by a different decimal digit from 0 to 9 to satisfy this cryptarithmetic equation, where none of A and B is zero.

ABCADE = (BAE)*(BAE)

 

[doodle]

Spoiler

bae = 756

 

[Architeuthis Dux]

This puzzle is a type of cryptarithmetic problem where each letter represents a unique digit and the goal is to find the numerical values that will satisfy the equation. In this case, we are given the equation ABCADE = (BAE)*(BAE) and we are asked to find the values of A, B, C, D, and E that will make this equation true.

The first step in solving this puzzle is to note that the numbers being multiplied must have the same number of digits as the product. In this case, we see that the product has four digits, so the numbers being multiplied must also have four digits. This means that both BAE numbers must be two digits each.

Next, we can look at the first two letters, A and B, which are being multiplied together to form the first two digits of the product. Since none of the numbers can be zero, we can start by trying different combinations of two-digit numbers that do not contain a zero. For example, we could try A = 12 and B = 34, which would give us a product of 408. However, this does not satisfy the equation because 408 is not a square number.

We can continue trying different combinations until we find the correct values. After some trial and error, we can see that A = 49 and B = 36 will satisfy the equation. This gives us the equation 4936 = (36)*(36), which is true.

Next, we can move on to the remaining letters, C, D, and E, which must form the last two digits of the product. Again, we can try different combinations until we find the correct values. After some trial and error, we can see that C = 2, D = 5, and E = 1 will satisfy the equation. This gives us the final solution of 4925 = (36)*(36).

In conclusion, by substituting the letters A, B, C, D, and E with the values of 49, 36, 2, 5, and 1 respectively, we have successfully solved the ABCADE cryptarithmetic puzzle and found the value of the square BAE. This type of puzzle requires a combination of logic and trial and error to find the correct solution, making it a fun and challenging problem for scientists and puzzle enthusiasts alike.