Given th alphametic where each letter represents a different digit the value of c in the least value for ABCD?

Question

is
ABCD
-BCDA
------------------
1512
------------------

Answer 1

The question asks for the *least value of ABCD*. The smallest value of ABCD is when *A* is the smallest. B must at least be 1 (or else it would be a 3-digit number), so A must at least be 2.

Let's try A = 2, then D = 4

2BC4
-BC42
--------
1512

That would mean C = 5 and now B would have to be 0... but we already said that B had to be at least 1 (or else you don't have a four digit number).

Back to the drawing board. Let's try A = 3 and D = 5
3BC5
BC53
-------
1512

So now C = 6 and B = 1. We have to borrow from the 3 to make 11 and subtract the 6 to get 5. Yay! This works!
3165
-1653
-------
1512

So the smallest value of ABCD is when C = 6
c) 6

Answer 2

ABCD = 1000A + 100B + 10C + D, and

BCDA = 1000B + 100C + 10D + A, so

ABCD - BCDA = 999A - 900B - 90C - 9D = 1512 =>

9999A - 9(1000A + 100B + 10C + D) = 1512 =>

1111A - 1000A - 100B - 10C - D = 168 =>

100(A - B) + 10(A - C) + (A - D) = 168

So A - D = 8, A must be 9 and D = 1, A - B = 1, so B = 8 and A - C = 6, so C = 3.

The number ABCD = 9831 and BCDA = 8319

9831 - 8319 = 1512 !!!

Answer 3

3