Find the digits that represent the letters E, F, G, and H to satisfy the following puzzle. Each letter represents a different digit.

EFGH x 4 = HGFE

2178 x 4 = 8712

To solve this puzzle, we need to find the values of the digits E, F, G, and H that make the equation EFGH x 4 = HGFE true.

Let's break it down step by step:

1. We know that each letter represents a different digit, so there are no repeated digits.

2. Since we are multiplying EFGH by 4, the first digit of the result (HGFE) must be 8 because the largest possible value for a product of a single digit number (4) and a four-digit number is 9,999 (9,999 x 4 = 39,996).

3. Therefore, H is equal to 8.

Next, we can focus on the other digits:

4. Multiplying 8 by 4 gives us 32 as a two-digit result. So, E must be 3 because the largest possible value for HGFE is 8,712 (8,712 divided by 4 equals 2,178).

5. Now let's focus on the second digit of the result (G). Since we know that E is 3 and H is 8, we need to find a digit for G that satisfies the equation EFGH x 4 = HGFE. The largest possible value of HGFE from our previous step is 8,712.

6. Dividing 8,712 by 4 gives us 2,178. Looking at the second digit of this result, G is equal to 1.

Finally, we have:

E = 3
F = ?
G = 1
H = 8

7. Now we need to find the value of F. We know that no digits are repeated, and since we have already used 3, 1, and 8, the only remaining digit is 2.

Thus, the solution to the puzzle is:

E = 3
F = 2
G = 1
H = 8