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Question:

Which digit does the letter A represent?

Explanation:

Units place of (F + F) is F ⇒ F = 0 

Units place of (H + H) or (H + H + 1) is also F. This is possible only when H is 5 and there is no carry over.

So, F = 0 and H = 5

∴ (1 + B + A) = (10A + A)
⇒ 1 + B = 10A
⇒ A = 1 and B = 9

As units place of (G + K) = 1, actual value of G + K = 11

So, 1 + F + A = 1 + 1 + 0 = 2 = C

Now, 1 + J = G and G + K = 11

Also, G, J and K ∈ {3, 4, 6, 7, 8}

Therefore, (G, J, K) = (8, 7, 3) or (7, 6, 4) or (4, 3, 7), accordingly D and E can be represented by (4,6) or (3, 8) or (6, 8) in some order.

The letter A represents digit 1.

Answer: 1.