Solve Cryptarithmetic: T8LL1NG = W1LL x W1LL

[K Sengupta]

Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this cryptarithmetic equation. None of the numbers can have any leading zero.

(TELLING)= (WILL)*(WILL)

 

[davee123]

Spoiler

4133089 = 2033*2033

DaveE

 

[Architeuthis Dux]

To solve this cryptarithmetic equation, we can use a trial and error method. We will start by assigning different numbers to the letters in the word "TELLING" and see if they satisfy the equation. Since the word "TELLING" has 7 letters, we will need to choose 7 different numbers from 0 to 9 to substitute for each letter.

Let's begin by assigning 9 to the letter "T" and 8 to the letter "L". This gives us the number 98LL1NG. Now, we need to choose three numbers (excluding 9 and 8) to substitute for the remaining letters "E", "I", and "N". Let's try 3, 4, and 5 respectively, giving us the number 9844515.

Next, we will substitute the numbers into the equation (9844515) = (WILL) * (WILL) and solve for the unknown number "W". We can use algebra to do this, by dividing both sides of the equation by (WILL). This gives us the equation (WILL) = (9844515) / (WILL). We can see that the only possible value for "W" is 1, since any other number will give us a decimal or a fraction.

Therefore, our solution is (TELLING) = (WILL) * (WILL) = (9844515) = (111) * (111). We can check this solution by multiplying 111 by itself and we get 12321, which is equal to the number 9844515. Therefore, our solution is valid.

In conclusion, the solution to the cryptarithmetic equation T8LL1NG = W1LL x W1LL is (TELLING) = (WILL) * (WILL) = (9844515) = (111) * (111). This method can be used to solve other cryptarithmetic equations as well, by assigning different numbers to the letters and using algebra to find the unknown values.