### Brain Teasers

# Circular System?

Given that:

a + b = 12

c + d = 7

b-c = 2

a-d = 3

Find (a-b) + (c - d).

a + b = 12

c + d = 7

b-c = 2

a-d = 3

Find (a-b) + (c - d).

### Hint

It doesn't hurt to "regroup".### Answer

The answer is 1. If you tried to get each letter individually, you'd probably go in circles. Instead, notice that (a-b) + (c-d) = (a+c) - (b+d).Also, (a+c) = [(a+b) - (b-c)], and (b+d) = [(a+b) - (a-d)], so:

(a+c) - (b+d)

= [(a+b) - (b-c)] - [(a+b) - (a-d)]

= [(12 - 2)] - [(12 - 3)]

= 10 - 9

= 1

or

(a-b) + (c-d)

= (a-d) - (b-c)

= 3 - 2

= 1

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