0-level algebra and the quant interview question
Apparently a position for a quant trader at a major bank required the candidate to solve this math riddle:
Given a four digit number described by the letters a1,a2,b1,b2, provide a formula to tell me if a1,a2 + b1,b2 = a2,b1.
For example, they use the number 1978. 19 + 78 = 97.
This doesn't really seem like a quantitative analysis problem, this seems to be algebra.
So, we know
a2 + b2 = (r * 10) + b1
where r is the "remainder" that will go into the adjacent left column. using the example above, 9 + 8 = (1 * 10) + 7
(r * 10) = a2 + b2 - b1
We also know that completing the addition in the adjacent left column means
r+ a1 + b1 = a2
r = a2 - a1 - b1
r * 10 = (a2 - a1 - b1) * 10
a2 + b2 - b1 = (a2 - a1 - b1) * 10
and solving for each now yields
a1 = (((a2 + b2 - b1) / 10) + b1 - a2) * (-1)
a2 = ((a2 - a1 - b1) * 10) - b2 + b1
b1 = (((a2 - a1 - b1) * 10) - a2 - b2) * (-1)
b2 = ((a2 - a1 - b1) * 10) - a2 + b1
Here's the haskell to find all such numbers from 1000 to 9999:
last update 2011-09-09