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

Question

is
ABCD
-BCDA
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1512
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a)1
b)2
c)6
d)7

Answer 1

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
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1512

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